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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 12696.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.m1 | 12696b1 | \([0, -1, 0, -196872, -33556500]\) | \(-778918741604594/27\) | \(-29251584\) | \([]\) | \(31680\) | \(1.3796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12696.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12696.m do not have complex multiplication.Modular form 12696.2.a.m
sage: E.q_eigenform(10)