The database currently contains data on all modular curves $X_H$ with $\det(H)=\widehat\Z^\times$ such that at least one of the following hold:

- $H$ has level at most $70$;
- $H$ has prime-power level at most $335$;
- $H$ contains $-I$ and has genus at most $24$ and level at most $335$;
- $H$ does not contain $-I$ and has genus at most $8$ and level at most $335$.

Information on rational cusps and rational CM points is available for every $X_H$.

Information on the analytic rank, and the isogeny decomposition of the Jacobian is available for every $X_H$ of level $N\le 70$.

Rational and low degree points data is available for points that correspond to elliptic curves in the LMFDB; **note that this excludes many known rational points**.

Plane models are available for a subset of the curves of genus $g\le 24$, as summarized in the following table. Note that the columns add to more than the total since some modular curves have models of multiple types.

Genus | 0 | 1 | 2 | 3 | 4 | 5 | 6-24 |
---|---|---|---|---|---|---|---|

Projective line | 1025 | 0 | 0 | 0 | 0 | 0 | 0 |

Canonical model | 0 | 0 | 0 | 1203 | 1341 | 6916 | 36792 |

plane model | 889 | 3012 | 1460 | 3640 | 1306 | 7386 | 29577 |

Weierstrass model | 0 | 1174 | 1457 | 2250 | 13 | 557 | 152 |

Double cover of conic | 0 | 0 | 0 | 1423 | 0 | 89 | 0 |

Embedded model | 0 | 3317 | 1460 | 3866 | 15 | 726 | 152 |

No model available | 223 | 233 | 5 | 110 | 43 | 324 | 60233 |

Total | 2137 | 4724 | 1465 | 5179 | 1399 | 7966 | 97177 |

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Andrew Sutherland on 2024-03-11 12:51:04

**Referred to by:**

**History:**(expand/hide all)

- 2024-03-11 12:51:04 by Andrew Sutherland
- 2024-03-11 12:50:55 by Andrew Sutherland
- 2024-03-11 08:05:51 by Andrew Sutherland
- 2024-03-10 23:29:16 by Andrew Sutherland
- 2023-07-09 16:20:12 by Andrew Sutherland
- 2023-07-05 03:45:22 by David Roe
- 2023-06-21 14:27:15 by Andrew Sutherland
- 2022-03-20 22:23:10 by Andrew Sutherland
- 2022-03-20 21:53:09 by Andrew Sutherland

**Differences**(show/hide)