Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 73638.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73638.f1 | 73638f1 | \([1, -1, 1, -602645, -207773971]\) | \(-33203218336044207625/6404524235292672\) | \(-4668898167528357888\) | \([]\) | \(1101120\) | \(2.3059\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 73638.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 73638.f do not have complex multiplication.Modular form 73638.2.a.f
sage: E.q_eigenform(10)