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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 77616fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.gb1 | 77616fn1 | \([0, 0, 0, -701211, -234299702]\) | \(-260607143968297/11270993184\) | \(-1649095260265119744\) | \([]\) | \(1612800\) | \(2.2613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77616fn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 77616fn do not have complex multiplication.Modular form 77616.2.a.fn
sage: E.q_eigenform(10)