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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 67158.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67158.k1 | 67158n1 | \([1, -1, 0, -8127, -280017]\) | \(-81436110288625/14259882\) | \(-10395453978\) | \([]\) | \(71424\) | \(0.92733\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67158.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 67158.k do not have complex multiplication.Modular form 67158.2.a.k
sage: E.q_eigenform(10)