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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 15680cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.z1 | 15680cm1 | \([0, -1, 0, -23781, 1422205]\) | \(-2249728/5\) | \(-3305767485440\) | \([]\) | \(43008\) | \(1.2850\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 15680cm do not have complex multiplication.Modular form 15680.2.a.cm
sage: E.q_eigenform(10)