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Explore curve fixtures
The catalog contains 12 handwritten illustrative entries with catalog-like labels and 148 deterministic synthetic fixtures. These values are not verified LMFDB or Cremona records. Generated regulator, period, and height values depend on rank; omitting a rank column does not make the remaining features independent.
Fixtures
160
12 illustrative · 148 synthetic
Rank 0 / 1
64 / 76
Rank 2+
20
⟨Ω_E⟩
0.897
| Label | N | r | R | Ω | Δ | Tors | Src |
|---|---|---|---|---|---|---|---|
| 11.a1 | 11 | 0 | 1.0000 | 0.2538 | 11 | Z/5 | illustrative |
| 11.a2 | 11 | 0 | 1.0000 | 1.2692 | -161051 | Z/5 | illustrative |
| 11.a3 | 11 | 0 | 1.0000 | 6.3460 | -11 | Z/5 | illustrative |
| 37.a1 | 37 | 1 | 0.0511 | 5.9869 | -37 | 1 | illustrative |
| 43.a1 | 43 | 1 | 0.0325 | 5.4711 | -43 | 1 | illustrative |
| 43.f1 | 43 | 2 | 2.2077 | 1.6495 | 11622 | Z/2 | synthetic |
| 53.a1 | 53 | 1 | 0.1430 | 4.8720 | -53 | 1 | illustrative |
| 61.a1 | 61 | 1 | 0.0486 | 4.9812 | -61 | 1 | illustrative |
| 89.a1 | 89 | 1 | 0.1723 | 4.2104 | -89 | 1 | illustrative |
| 389.a1 | 389 | 2 | 0.1525 | 2.4901 | -389 | 1 | illustrative |
| 433.a1 | 433 | 2 | 0.2341 | 2.3188 | -433 | 1 | illustrative |
| 810.a1 | 810 | 1 | 1.0087 | 1.2093 | 16745 | Z/2×Z/2 | synthetic |
| 851.f1 | 851 | 1 | 1.3374 | 1.4022 | -33887 | Z/5 | synthetic |
| 990.f1 | 990 | 0 | 1.0000 | 1.7548 | 2098801 | Z/2 | synthetic |
| 1421.e1 | 1421 | 1 | 1.2148 | 0.8852 | 483625 | Z/2 | synthetic |
| 1508.a1 | 1508 | 1 | 0.6670 | 1.0016 | 1905873 | 1 | synthetic |
| 1577.f1 | 1577 | 0 | 1.0000 | 1.8743 | 63430 | Z/2 | synthetic |
| 1585.c1 | 1585 | 1 | 0.4860 | 1.4635 | 217534 | 1 | synthetic |
| 1592.b1 | 1592 | 1 | 1.9064 | 1.4429 | -7650 | 1 | synthetic |
| 1631.b1 | 1631 | 4 | 17.9188 | 0.6847 | -6345666 | Z/5 | synthetic |
| 1871.d1 | 1871 | 0 | 1.0000 | 1.1711 | -61105 | Z/3 | synthetic |
| 2135.a1 | 2135 | 0 | 1.0000 | 1.1859 | 35859 | Z/5 | synthetic |
| 2183.d1 | 2183 | 3 | 6.7497 | 1.0046 | -609483 | Z/5 | synthetic |
| 2258.e1 | 2258 | 0 | 1.0000 | 1.7884 | -51523 | Z/4 | synthetic |
| 2467.b1 | 2467 | 0 | 1.0000 | 1.1858 | 93977 | Z/6 | synthetic |
| 2473.f1 | 2473 | 1 | 0.9681 | 1.4262 | 107937 | 1 | synthetic |
| 3024.b1 | 3024 | 0 | 1.0000 | 0.8911 | 27328 | Z/2 | synthetic |
| 3425.e1 | 3425 | 1 | 1.2811 | 0.7093 | 827962 | Z/5 | synthetic |
| 3610.d1 | 3610 | 0 | 1.0000 | 0.8985 | -105288 | Z/4 | synthetic |
| 3858.d1 | 3858 | 1 | 0.5998 | 0.9602 | -1509204 | Z/4 | synthetic |
| 4034.e1 | 4034 | 1 | 1.1957 | 0.6060 | -1355579 | Z/3 | synthetic |
| 5077.a1 | 5077 | 3 | 0.4172 | 1.1024 | -5077 | 1 | illustrative |
| 5450.a1 | 5450 | 0 | 1.0000 | 0.6013 | 1446739 | Z/6 | synthetic |
| 6288.c1 | 6288 | 0 | 1.0000 | 0.6152 | 1909383 | Z/6 | synthetic |
| 6587.d1 | 6587 | 1 | 1.5441 | 1.1538 | 26654434 | Z/4 | synthetic |
| 7021.e1 | 7021 | 0 | 1.0000 | 1.0848 | -18130071 | Z/2 | synthetic |
| 7211.e1 | 7211 | 1 | 1.4589 | 0.7082 | -1709162 | Z/4 | synthetic |
| 7873.c1 | 7873 | 2 | 1.8589 | 0.3916 | -86006 | Z/2×Z/2 | synthetic |
| 7948.d1 | 7948 | 0 | 1.0000 | 1.0879 | -2255449 | 1 | synthetic |
| 8981.d1 | 8981 | 1 | 0.6677 | 0.6130 | 2001235 | Z/2 | synthetic |
| 9040.d1 | 9040 | 0 | 1.0000 | 0.6339 | 289753 | Z/6 | synthetic |
| 9854.f1 | 9854 | 1 | 0.5900 | 1.0376 | 3999977 | Z/6 | synthetic |
| 11416.d1 | 11416 | 1 | 1.6213 | 0.9570 | 3432671 | Z/3 | synthetic |
| 11736.c1 | 11736 | 0 | 1.0000 | 1.2025 | 1129415 | Z/3 | synthetic |
| 12434.f1 | 12434 | 0 | 1.0000 | 1.1473 | 40782836 | Z/2 | synthetic |
| 14285.e1 | 14285 | 0 | 1.0000 | 0.7409 | -213004 | Z/3 | synthetic |
| 14389.c1 | 14389 | 1 | 0.8260 | 0.9120 | -5326766 | Z/4 | synthetic |
| 14532.c1 | 14532 | 1 | 2.0586 | 0.7690 | 112179 | Z/5 | synthetic |
| 15210.b1 | 15210 | 1 | 1.7003 | 0.5268 | 152974 | Z/2 | synthetic |
| 17126.d1 | 17126 | 1 | 1.5067 | 0.5112 | 2070750 | Z/6 | synthetic |
| 17408.d1 | 17408 | 0 | 1.0000 | 0.7331 | -6505841 | Z/2×Z/2 | synthetic |
| 17622.e1 | 17622 | 1 | 2.2854 | 0.8130 | -4694781 | Z/5 | synthetic |
| 17807.c1 | 17807 | 0 | 1.0000 | 0.9823 | 47617805 | Z/4 | synthetic |
| 17866.c1 | 17866 | 0 | 1.0000 | 1.0638 | -291623 | Z/2 | synthetic |
| 18071.e1 | 18071 | 1 | 1.2151 | 0.5184 | 36372837 | Z/6 | synthetic |
| 18924.d1 | 18924 | 1 | 2.1686 | 0.6477 | -496251 | Z/4 | synthetic |
| 19091.d1 | 19091 | 0 | 1.0000 | 0.7789 | 184860 | Z/2 | synthetic |
| 19577.d1 | 19577 | 1 | 1.6899 | 0.4321 | -624866 | Z/4 | synthetic |
| 19617.e1 | 19617 | 0 | 1.0000 | 0.5251 | -61561433 | Z/2×Z/2 | synthetic |
| 19789.e1 | 19789 | 2 | 5.1269 | 0.6448 | 724530 | Z/2 | synthetic |
| 19823.d1 | 19823 | 0 | 1.0000 | 1.0918 | -615510 | Z/5 | synthetic |
| 20352.e1 | 20352 | 0 | 1.0000 | 0.4445 | -64225575 | Z/3 | synthetic |
| 20828.b1 | 20828 | 0 | 1.0000 | 0.9642 | -283359 | Z/5 | synthetic |
| 22135.c1 | 22135 | 1 | 1.8576 | 0.5309 | 78084660 | 1 | synthetic |
| 25372.a1 | 25372 | 1 | 1.2699 | 0.4289 | 263769 | Z/4 | synthetic |
| 25952.c1 | 25952 | 1 | 2.6875 | 0.7005 | -923473 | Z/2×Z/2 | synthetic |
| 27229.e1 | 27229 | 0 | 1.0000 | 0.8843 | -95338626 | Z/3 | synthetic |
| 27266.b1 | 27266 | 1 | 1.7853 | 0.3690 | -852609 | Z/4 | synthetic |
| 27813.f1 | 27813 | 1 | 2.0104 | 0.6946 | 513168 | Z/5 | synthetic |
| 29588.f1 | 29588 | 3 | 7.3225 | 0.3588 | -55567595 | 1 | synthetic |
| 29633.c1 | 29633 | 1 | 0.9586 | 0.5526 | -3636964 | 1 | synthetic |
| 30154.c1 | 30154 | 1 | 0.9142 | 0.8376 | 11647000 | Z/3 | synthetic |
| 30404.b1 | 30404 | 1 | 0.4407 | 0.6795 | -138178 | Z/2 | synthetic |
| 31933.c1 | 31933 | 1 | 1.7053 | 0.4790 | 79136109 | Z/3 | synthetic |
| 32863.e1 | 32863 | 0 | 1.0000 | 0.8373 | -364053 | Z/5 | synthetic |
| 34294.b1 | 34294 | 1 | 1.1977 | 0.7354 | -8015246 | Z/4 | synthetic |
| 34831.d1 | 34831 | 0 | 1.0000 | 0.7992 | -45240449 | Z/6 | synthetic |
| 35002.a1 | 35002 | 2 | 5.6670 | 0.6676 | -10273599 | Z/3 | synthetic |
| 35268.d1 | 35268 | 2 | 1.6442 | 0.6421 | -43563414 | Z/4 | synthetic |
| 35418.a1 | 35418 | 2 | 5.9196 | 0.6550 | 7728027 | Z/2 | synthetic |
Showing 80 of 160 matches