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SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 162288.gj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.gj1 | 162288cq1 | \([0, 0, 0, 64181229, -132809556782]\) | \(83228502970940543/69854999176704\) | \(-24539923709313415762673664\) | \([]\) | \(36495360\) | \(3.5595\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162288.gj1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162288.gj do not have complex multiplication.Modular form 162288.2.a.gj
sage: E.q_eigenform(10)