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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 206400.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.r1 | 206400ic1 | \([0, -1, 0, -79553, 8662977]\) | \(-3398434606474/387\) | \(-6340608000\) | \([]\) | \(479232\) | \(1.3044\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 206400.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 206400.r do not have complex multiplication.Modular form 206400.2.a.r
sage: E.q_eigenform(10)