Show commands:
SageMath
E = EllipticCurve("nz1")
E.isogeny_class()
Elliptic curves in class 458640.nz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 458640.nz1 | 458640nz1 | \([0, 0, 0, -2837982, -1840484149]\) | \(-767228471296/142155\) | \(-468371057867884080\) | \([]\) | \(8881152\) | \(2.3931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640.nz1 has rank \(0\).
Complex multiplication
The elliptic curves in class 458640.nz do not have complex multiplication.Modular form 458640.2.a.nz
sage: E.q_eigenform(10)