Properties

Label 169050gv
Number of curves $4$
Conductor $169050$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gv1")
 
E.isogeny_class()
 

Elliptic curves in class 169050gv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.eg4 169050gv1 \([1, 0, 1, -733801, 394606748]\) \(-23771111713777/22848457968\) \(-42001534866831750000\) \([2]\) \(5898240\) \(2.4615\) \(\Gamma_0(N)\)-optimal
169050.eg3 169050gv2 \([1, 0, 1, -13694301, 19498383748]\) \(154502321244119857/55101928644\) \(101291981297468062500\) \([2, 2]\) \(11796480\) \(2.8081\)  
169050.eg1 169050gv3 \([1, 0, 1, -219090051, 1248175760248]\) \(632678989847546725777/80515134\) \(148008203124468750\) \([2]\) \(23592960\) \(3.1547\)  
169050.eg2 169050gv4 \([1, 0, 1, -15666551, 13514577248]\) \(231331938231569617/90942310746882\) \(167176123704061256531250\) \([2]\) \(23592960\) \(3.1547\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050gv have rank \(1\).

Complex multiplication

The elliptic curves in class 169050gv do not have complex multiplication.

Modular form 169050.2.a.gv

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4 q^{11} + q^{12} + 2 q^{13} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.