Properties

Label 169050ia
Number of curves $6$
Conductor $169050$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("169050.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 169050ia

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
169050.e5 169050ia1 [1, 1, 0, 154325, -47727875] [2] 3145728 \(\Gamma_0(N)\)-optimal
169050.e4 169050ia2 [1, 1, 0, -1413675, -554191875] [2, 2] 6291456  
169050.e3 169050ia3 [1, 1, 0, -6215675, 5424298125] [2, 2] 12582912  
169050.e2 169050ia4 [1, 1, 0, -21699675, -38915017875] [2] 12582912  
169050.e1 169050ia5 [1, 1, 0, -96939175, 367320339625] [2] 25165824  
169050.e6 169050ia6 [1, 1, 0, 7675825, 26247656625] [2] 25165824  

Rank

sage: E.rank()
 

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

Modular form 169050.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} - 2q^{13} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.