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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 112710cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.cr1 | 112710cm1 | \([1, 0, 0, -1281, 18765]\) | \(-804441463921/66832740\) | \(-19314661860\) | \([]\) | \(120960\) | \(0.71921\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710cm do not have complex multiplication.Modular form 112710.2.a.cm
sage: E.q_eigenform(10)