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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 83490k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83490.p1 | 83490k1 | \([1, 1, 0, -523932, -145998486]\) | \(1086373192042242841/1626922968750\) | \(23819779185468750\) | \([]\) | \(1209600\) | \(2.0430\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83490k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 83490k do not have complex multiplication.Modular form 83490.2.a.k
sage: E.q_eigenform(10)