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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 116688z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.r1 | 116688z1 | \([0, 1, 0, -824, -29100]\) | \(-15124197817/78881088\) | \(-323096936448\) | \([]\) | \(117504\) | \(0.89267\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116688z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 116688z do not have complex multiplication.Modular form 116688.2.a.z
sage: E.q_eigenform(10)