↑

Properties

Label 136710.gq
Number of curves $2$
Conductor $136710$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gq1")
 
E.isogeny_class()
 

Elliptic curves in class 136710.gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
136710.gq1 136710v2 \([1, -1, 1, -16512152, 24096109979]\) \(5805223604235668521/435937500000000\) \(37388668373437500000000\) \([2]\) \(15482880\) \(3.0767\)  
136710.gq2 136710v1 \([1, -1, 1, 986728, 1669545371]\) \(1238798620042199/14760960000000\) \(-1265990281436160000000\) \([2]\) \(7741440\) \(2.7301\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 136710.gq have rank \(1\).

Complex multiplication

The elliptic curves in class 136710.gq do not have complex multiplication.

Modular form 136710.2.a.gq

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4 q^{11} + 4 q^{13} + q^{16} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.