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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 225400.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225400.z1 | 225400bw1 | \([0, -1, 0, -220908, -78684563]\) | \(-40535147776/67648175\) | \(-1989685035143750000\) | \([]\) | \(2211840\) | \(2.2020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 225400.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 225400.z do not have complex multiplication.Modular form 225400.2.a.z
sage: E.q_eigenform(10)