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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 257600.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.ep1 | 257600ep1 | \([0, 1, 0, 167, 6463]\) | \(32000/1127\) | \(-18032000000\) | \([]\) | \(110592\) | \(0.64788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257600.ep1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257600.ep do not have complex multiplication.Modular form 257600.2.a.ep
sage: E.q_eigenform(10)