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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 116688r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116688.i1 | 116688r1 | \([0, -1, 0, -37720, -5870096]\) | \(-1449073218392281/2811246362496\) | \(-11514865100783616\) | \([]\) | \(838656\) | \(1.7715\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116688r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 116688r do not have complex multiplication.Modular form 116688.2.a.r
sage: E.q_eigenform(10)