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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 409101.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.e1 | 409101e1 | \([1, 1, 1, 180711, -51384684]\) | \(1268071343/2956581\) | \(-1521680316784812261\) | \([]\) | \(5464800\) | \(2.1729\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 409101.e do not have complex multiplication.Modular form 409101.2.a.e
sage: E.q_eigenform(10)