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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5586i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.e1 | 5586i1 | \([1, 1, 0, -53, 141]\) | \(-346016041/34656\) | \(-1698144\) | \([]\) | \(960\) | \(-0.064333\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5586i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5586i do not have complex multiplication.Modular form 5586.2.a.i
sage: E.q_eigenform(10)