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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 51376z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51376.a1 | 51376z1 | \([0, 0, 0, -165451, 25911418]\) | \(-25334470953/9386\) | \(-185566942306304\) | \([]\) | \(612864\) | \(1.7054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51376z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 51376z do not have complex multiplication.Modular form 51376.2.a.z
sage: E.q_eigenform(10)