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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 355740f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.f1 | 355740f1 | \([0, -1, 0, -2362145221, -44187364314575]\) | \(1005720267120902144/5811307335\) | \(8422482859039571706236160\) | \([]\) | \(225358848\) | \(3.9732\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 355740f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 355740f do not have complex multiplication.Modular form 355740.2.a.f
sage: E.q_eigenform(10)