Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 12600cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12600.cf1 | 12600cn1 | \([0, 0, 0, -6375, -210625]\) | \(-6288640/567\) | \(-2583393750000\) | \([]\) | \(15360\) | \(1.1249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12600cn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12600cn do not have complex multiplication.Modular form 12600.2.a.cn
sage: E.q_eigenform(10)