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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 68970.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68970.k1 | 68970q1 | \([1, 1, 0, 7582463, 81276661]\) | \(3292939724890125839639/1905816470814720000\) | \(-27903058949198315520000\) | \([]\) | \(7257600\) | \(2.9964\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68970.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 68970.k do not have complex multiplication.Modular form 68970.2.a.k
sage: E.q_eigenform(10)