Properties

Label 262080o
Number of curves 4
Conductor 262080
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.o3 262080o1 [0, 0, 0, -11703, 450452] [2] 524288 \(\Gamma_0(N)\)-optimal
262080.o2 262080o2 [0, 0, 0, -39828, -2542048] [2, 2] 1048576  
262080.o4 262080o3 [0, 0, 0, 77172, -14663248] [2] 2097152  
262080.o1 262080o4 [0, 0, 0, -606828, -181940848] [2] 2097152  

Rank

sage: E.rank()
 

The elliptic curves in class 262080o have rank \(1\).

Modular form 262080.2.a.o

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

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.