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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 49725.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.a1 | 49725v1 | \([0, 0, 1, -52875, 4602656]\) | \(57409966080/1085773\) | \(309190826953125\) | \([]\) | \(268800\) | \(1.5740\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49725.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49725.a do not have complex multiplication.Modular form 49725.2.a.a
sage: E.q_eigenform(10)