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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 141570.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.w1 | 141570ee1 | \([1, -1, 0, -2338650, 1377877716]\) | \(-822920371811/505440\) | \(-868822988004560160\) | \([]\) | \(2956800\) | \(2.3849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 141570.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 141570.w do not have complex multiplication.Modular form 141570.2.a.w
sage: E.q_eigenform(10)