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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 8712.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8712.m1 | 8712v1 | \([0, 0, 0, -660, -7436]\) | \(-1408000/243\) | \(-5487305472\) | \([]\) | \(3840\) | \(0.59501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8712.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8712.m do not have complex multiplication.Modular form 8712.2.a.m
sage: E.q_eigenform(10)