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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 166635.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166635.z1 | 166635x1 | \([0, 0, 1, 138872022, -1417334891571]\) | \(2744564518708084736/9629735831296875\) | \(-1039223401868845259975671875\) | \([]\) | \(39536640\) | \(3.8670\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 166635.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 166635.z do not have complex multiplication.Modular form 166635.2.a.z
sage: E.q_eigenform(10)