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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 36414.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36414.z1 | 36414bf1 | \([1, -1, 0, -1737, 23949]\) | \(2751936625/458752\) | \(96650330112\) | \([]\) | \(34560\) | \(0.82908\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 36414.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 36414.z do not have complex multiplication.Modular form 36414.2.a.z
sage: E.q_eigenform(10)