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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 77616p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.gg1 | 77616p1 | \([0, 0, 0, -654591, 203862393]\) | \(-610325920583424/55240493\) | \(-2807563144733424\) | \([]\) | \(737280\) | \(2.0037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77616p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 77616p do not have complex multiplication.Modular form 77616.2.a.p
sage: E.q_eigenform(10)