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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 213444z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.ba1 | 213444z1 | \([0, 0, 0, -1565256, -753996859]\) | \(-70647808/27\) | \(-162085780435038768\) | \([]\) | \(3535488\) | \(2.2682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 213444z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 213444z do not have complex multiplication.Modular form 213444.2.a.z
sage: E.q_eigenform(10)