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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 39039.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.z1 | 39039f1 | \([0, -1, 1, -53460, 33664529]\) | \(-1593413632/45196767\) | \(-479289087313127091\) | \([]\) | \(808704\) | \(2.0731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39039.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 39039.z do not have complex multiplication.Modular form 39039.2.a.z
sage: E.q_eigenform(10)