Properties

Label 262080.k
Number of curves 2
Conductor 262080
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.k1 262080k1 [0, 0, 0, -32763, -2051012] [2] 1105920 \(\Gamma_0(N)\)-optimal
262080.k2 262080k2 [0, 0, 0, 44412, -10262432] [2] 2211840  

Rank

sage: E.rank()
 

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

Modular form 262080.2.a.k

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.