Properties

Label 116886.q
Number of curves $1$
Conductor $116886$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.q1 116886r1 \([1, 0, 1, -275157, -58972256]\) \(-977077413467/71221248\) \(-167935977271738368\) \([]\) \(1330560\) \(2.0546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 116886.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 116886.q do not have complex multiplication.

Modular form 116886.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 2q^{10} + q^{12} - q^{13} - q^{14} - 2q^{15} + q^{16} + 3q^{17} - q^{18} - q^{19} + O(q^{20})\)  Toggle raw display