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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 206400.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.k1 | 206400cs1 | \([0, -1, 0, -2083, -55463]\) | \(-40000000/31347\) | \(-783675000000\) | \([]\) | \(288000\) | \(0.98089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 206400.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 206400.k do not have complex multiplication.Modular form 206400.2.a.k
sage: E.q_eigenform(10)