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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 41650m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.ba1 | 41650m1 | \([1, 1, 0, -17000, -1156000]\) | \(-709731835729/334084000\) | \(-255783062500000\) | \([]\) | \(207360\) | \(1.4706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41650m do not have complex multiplication.Modular form 41650.2.a.m
sage: E.q_eigenform(10)