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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 47775.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47775.cm1 | 47775bh1 | \([1, 1, 0, 118800, -4485375]\) | \(1680455/1053\) | \(-116190014530078125\) | \([]\) | \(604800\) | \(1.9636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47775.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47775.cm do not have complex multiplication.Modular form 47775.2.a.cm
sage: E.q_eigenform(10)