Properties

Label 262080m
Number of curves 4
Conductor 262080
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.m4 262080m1 [0, 0, 0, 350232, 86710808] [2] 5898240 \(\Gamma_0(N)\)-optimal
262080.m3 262080m2 [0, 0, 0, -2113788, 838729712] [2, 2] 11796480  
262080.m1 262080m3 [0, 0, 0, -31008108, 66451951568] [2] 23592960  
262080.m2 262080m4 [0, 0, 0, -12643788, -16645282288] [2] 23592960  

Rank

sage: E.rank()
 

The elliptic curves in class 262080m have rank \(0\).

Modular form 262080.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 4q^{11} + q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.