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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 400710.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.k1 | 400710k1 | \([1, 1, 0, 422363, 118462861]\) | \(177116123227679/230977680000\) | \(-10866548446936080000\) | \([]\) | \(8709120\) | \(2.3386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400710.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400710.k do not have complex multiplication.Modular form 400710.2.a.k
sage: E.q_eigenform(10)