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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 493680i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.i1 | 493680i1 | \([0, -1, 0, -62476, 6730495]\) | \(-951468070144/135517455\) | \(-3841239009556080\) | \([]\) | \(2970240\) | \(1.7213\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 493680i do not have complex multiplication.Modular form 493680.2.a.i
sage: E.q_eigenform(10)