Show commands:
SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 405600ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405600.ez1 | 405600ez1 | \([0, 1, 0, 11267, 752363]\) | \(12800/27\) | \(-333629038080000\) | \([]\) | \(1292544\) | \(1.4711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405600ez1 has rank \(0\).
Complex multiplication
The elliptic curves in class 405600ez do not have complex multiplication.Modular form 405600.2.a.ez
sage: E.q_eigenform(10)