Properties

Label 232050.fv
Number of curves 4
Conductor 232050
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("232050.fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 232050.fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
232050.fv1 232050fv3 [1, 0, 0, -23782688, 44639593992] [2] 10616832  
232050.fv2 232050fv2 [1, 0, 0, -1487688, 696148992] [2, 2] 5308416  
232050.fv3 232050fv4 [1, 0, 0, -824688, 1320031992] [2] 10616832  
232050.fv4 232050fv1 [1, 0, 0, -135688, -131008] [2] 2654208 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 232050.fv have rank \(1\).

Modular form 232050.2.a.fv

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.