Properties

Label 116610.r
Number of curves $1$
Conductor $116610$
CM no
Rank $1$

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Show commands: 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)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 3 q^{11} - q^{12} - q^{14} - q^{15} + q^{16} + 2 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display