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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 12138z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12138.z1 | 12138z1 | \([1, 0, 0, -91, -343]\) | \(-288568081/1176\) | \(-339864\) | \([]\) | \(1728\) | \(-0.082518\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12138z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12138z do not have complex multiplication.Modular form 12138.2.a.z
sage: E.q_eigenform(10)