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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 39039b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.m1 | 39039b1 | \([0, -1, 1, -5800019, -5374475299]\) | \(127680722384510660804608/1761798128013\) | \(297743883634197\) | \([]\) | \(625152\) | \(2.3326\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39039b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 39039b do not have complex multiplication.Modular form 39039.2.a.b
sage: E.q_eigenform(10)