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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 489762.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.k1 | 489762k1 | \([1, -1, 0, -341496, -21207744]\) | \(7406396257/3956736\) | \(2352943079253172224\) | \([]\) | \(9345024\) | \(2.2165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 489762.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 489762.k do not have complex multiplication.Modular form 489762.2.a.k
sage: E.q_eigenform(10)