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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2205m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2205.m1 | 2205m1 | \([0, 0, 1, -136857, 32113975]\) | \(-1376628736/1366875\) | \(-281472991507141875\) | \([]\) | \(37632\) | \(2.0440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2205m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 2205m do not have complex multiplication.Modular form 2205.2.a.m
sage: E.q_eigenform(10)