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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 32368z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32368.bb1 | 32368z1 | \([0, 1, 0, -19136, 1012532]\) | \(654699641761/112\) | \(132579328\) | \([]\) | \(48384\) | \(0.95719\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32368z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 32368z do not have complex multiplication.Modular form 32368.2.a.z
sage: E.q_eigenform(10)