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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 141570.ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.ef1 | 141570k1 | \([1, -1, 1, -624317, 190034309]\) | \(-305088363822419089/15974400000\) | \(-1409085849600000\) | \([]\) | \(1305600\) | \(1.9753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 141570.ef1 has rank \(1\).
Complex multiplication
The elliptic curves in class 141570.ef do not have complex multiplication.Modular form 141570.2.a.ef
sage: E.q_eigenform(10)