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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6440k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6440.g1 | 6440k1 | \([0, -1, 0, -180, 1897]\) | \(-40535147776/67648175\) | \(-1082370800\) | \([]\) | \(1920\) | \(0.42434\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6440k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6440k do not have complex multiplication.Modular form 6440.2.a.k
sage: E.q_eigenform(10)