Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1856c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1856.e1 | 1856c1 | \([0, -1, 0, -321, -2111]\) | \(-55990084/29\) | \(-1900544\) | \([]\) | \(256\) | \(0.15584\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1856c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1856c do not have complex multiplication.Modular form 1856.2.a.c
sage: E.q_eigenform(10)