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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 100011.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100011.e1 | 100011c1 | \([0, -1, 1, 9022524, -11690123677]\) | \(81228381874428716689043456/106013477073021185065059\) | \(-106013477073021185065059\) | \([]\) | \(10765440\) | \(3.1040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100011.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100011.e do not have complex multiplication.Modular form 100011.2.a.e
sage: E.q_eigenform(10)