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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 16650.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16650.r1 | 16650bj1 | \([1, -1, 0, -117, 39541]\) | \(-625/2368\) | \(-674325000000\) | \([]\) | \(25920\) | \(0.94869\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 16650.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 16650.r do not have complex multiplication.Modular form 16650.2.a.r
sage: E.q_eigenform(10)