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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 141570ex
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.l1 | 141570ex1 | \([1, -1, 0, 20850, 1777870]\) | \(20956092093/40842230\) | \(-1953571549167810\) | \([]\) | \(806400\) | \(1.6186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 141570ex1 has rank \(1\).
Complex multiplication
The elliptic curves in class 141570ex do not have complex multiplication.Modular form 141570.2.a.ex
sage: E.q_eigenform(10)