Properties

Label 106722bx
Number of curves $1$
Conductor $106722$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 106722bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106722.j1 106722bx1 \([1, -1, 0, -259842501, 1671401614581]\) \(-260607143968297/11270993184\) \(-83913173617662394090104096\) \([]\) \(56448000\) \(3.7400\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 106722bx1 has rank \(1\).

Complex multiplication

The elliptic curves in class 106722bx do not have complex multiplication.

Modular form 106722.2.a.bx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - 6 q^{13} + q^{16} - 5 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display