Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 10780a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10780.j1 | 10780a1 | \([0, -1, 0, -355266, 85805105]\) | \(-129084391106508544/7863818359375\) | \(-302096446093750000\) | \([]\) | \(102960\) | \(2.1089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10780a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 10780a do not have complex multiplication.Modular form 10780.2.a.a
sage: E.q_eigenform(10)