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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 188760cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.c1 | 188760cm1 | \([0, -1, 0, -216, -2484]\) | \(-4518338/8775\) | \(-2174515200\) | \([]\) | \(96768\) | \(0.48129\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 188760cm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 188760cm do not have complex multiplication.Modular form 188760.2.a.cm
sage: E.q_eigenform(10)