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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 111012e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111012.f1 | 111012e1 | \([0, 1, 0, -284750845, 1849368130751]\) | \(-11859948880710132130963456/375913713056211\) | \(-80932718766150003456\) | \([]\) | \(11923200\) | \(3.3230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111012e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 111012e do not have complex multiplication.Modular form 111012.2.a.e
sage: E.q_eigenform(10)