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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 122694z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122694.x1 | 122694z1 | \([1, 1, 0, -603671, 253487733]\) | \(-16835377/9504\) | \(-13734389419269371424\) | \([]\) | \(4492800\) | \(2.3754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 122694z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 122694z do not have complex multiplication.Modular form 122694.2.a.z
sage: E.q_eigenform(10)