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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 76440cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.bz1 | 76440cm1 | \([0, 1, 0, -16921, 841595]\) | \(-17790954496/195\) | \(-5873038080\) | \([]\) | \(112320\) | \(1.0287\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440cm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 76440cm do not have complex multiplication.Modular form 76440.2.a.cm
sage: E.q_eigenform(10)