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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 4998.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.z1 | 4998bc1 | \([1, 1, 1, 2694, -49785]\) | \(53582633/58752\) | \(-2370855118464\) | \([]\) | \(9408\) | \(1.0611\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4998.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4998.z do not have complex multiplication.Modular form 4998.2.a.z
sage: E.q_eigenform(10)