Properties

Label 371280.fv
Number of curves 4
Conductor 371280
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("371280.fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 371280.fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
371280.fv1 371280fv4 [0, 1, 0, -15220920, -22861560492] [2] 10616832  
371280.fv2 371280fv2 [0, 1, 0, -952120, -356809132] [2, 2] 5308416  
371280.fv3 371280fv3 [0, 1, 0, -527800, -676067500] [2] 10616832  
371280.fv4 371280fv1 [0, 1, 0, -86840, 32340] [2] 2654208 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 371280.fv have rank \(0\).

Modular form 371280.2.a.fv

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} + q^{13} + q^{15} + q^{17} + 4q^{19} + O(q^{20}) \)

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.