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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 489762.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 489762.z1 | 489762z1 | \([1, -1, 0, -26590834620, -1669354023751088]\) | \(-3496594517361034456836001/970390721063183616\) | \(-577060013934999299415963942144\) | \([]\) | \(1230028800\) | \(4.6926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 489762.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 489762.z do not have complex multiplication.Modular form 489762.2.a.z
sage: E.q_eigenform(10)