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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 450800.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450800.et1 | 450800et1 | \([0, 1, 0, -220908, 78684563]\) | \(-40535147776/67648175\) | \(-1989685035143750000\) | \([]\) | \(4423680\) | \(2.2020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450800.et1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450800.et do not have complex multiplication.Modular form 450800.2.a.et
sage: E.q_eigenform(10)