Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("262080.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.n3 262080n1 [0, 0, 0, -1152108, 435455568] [2] 5898240 \(\Gamma_0(N)\)-optimal
262080.n2 262080n2 [0, 0, 0, -4101228, -2710665648] [2, 2] 11796480  
262080.n4 262080n3 [0, 0, 0, 7418772, -15193737648] [2] 23592960  
262080.n1 262080n4 [0, 0, 0, -62807148, -191579351472] [2] 23592960  

Rank

sage: E.rank()
 

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

Modular form 262080.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 4q^{11} + q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.