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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 126350z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126350.c1 | 126350z1 | \([1, -1, 0, -173167, -109888259]\) | \(-781229961/6650000\) | \(-4888361072656250000\) | \([]\) | \(4147200\) | \(2.2688\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 126350z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 126350z do not have complex multiplication.Modular form 126350.2.a.z
sage: E.q_eigenform(10)