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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 177600cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177600.bd1 | 177600cm1 | \([0, -1, 0, -16208, 799662]\) | \(-18836438080/333\) | \(-8325000000\) | \([]\) | \(268800\) | \(1.0312\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177600cm1 has rank \(2\).
Complex multiplication
The elliptic curves in class 177600cm do not have complex multiplication.Modular form 177600.2.a.cm
sage: E.q_eigenform(10)