Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.x1 116886x1 \([1, 0, 1, 1100613, -298150778]\) \(83228502970940543/69854999176704\) \(-123752392196480914944\) \([]\) \(5068800\) \(2.5431\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 116886.x1 has rank \(1\).

Complex multiplication

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

Modular form 116886.2.a.x

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