Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("262080.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.b1 262080b4 [0, 0, 0, -80991468, 280547898192] [2] 15925248  
262080.b2 262080b3 [0, 0, 0, -5063148, 4381412688] [2] 7962624  
262080.b3 262080b2 [0, 0, 0, -1023468, 365741392] [2] 5308416  
262080.b4 262080b1 [0, 0, 0, -224748, -34577072] [2] 2654208 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 262080.2.a.b

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.