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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 116610.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116610.r1 | 116610s1 | \([1, 1, 0, -7582, -300074]\) | \(-285284281827649/60256406250\) | \(-10183332656250\) | \([]\) | \(274176\) | \(1.2175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116610.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116610.r do not have complex multiplication.Modular form 116610.2.a.r
sage: E.q_eigenform(10)