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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 77658e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77658.k1 | 77658e1 | \([1, 1, 0, -47624731, -25636634723]\) | \(1889777177808124753/1048775180673024\) | \(6629688673814752864690176\) | \([]\) | \(21141120\) | \(3.4532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77658e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 77658e do not have complex multiplication.Modular form 77658.2.a.e
sage: E.q_eigenform(10)