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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 409101.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.m1 | 409101m1 | \([1, 0, 0, -15590429, 23709911490]\) | \(-5862183923791/4979799\) | \(-356000235061073984073\) | \([]\) | \(23224320\) | \(2.8707\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101.m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101.m do not have complex multiplication.Modular form 409101.2.a.m
sage: E.q_eigenform(10)