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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 413712.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
413712.i1 | 413712i1 | \([0, 0, 0, -8112, -500240]\) | \(-692224/867\) | \(-73940091383808\) | \([]\) | \(1674240\) | \(1.3546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 413712.i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 413712.i do not have complex multiplication.Modular form 413712.2.a.i
sage: E.q_eigenform(10)