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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 122694.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.z1 | 122694k1 | \([1, 1, 0, -4340261, -3484541133]\) | \(-1407450852604763/1119214746\) | \(-7190375861679859134\) | \([]\) | \(5419008\) | \(2.5486\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 122694.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 122694.z do not have complex multiplication.Modular form 122694.2.a.z
sage: E.q_eigenform(10)