Properties

Label 14784.w
Number of curves 6
Conductor 14784
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14784.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14784.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14784.w1 14784br5 [0, -1, 0, -289217, 59962977] [2] 81920  
14784.w2 14784br3 [0, -1, 0, -18177, 930465] [2, 2] 40960  
14784.w3 14784br2 [0, -1, 0, -2497, -26015] [2, 2] 20480  
14784.w4 14784br1 [0, -1, 0, -2177, -38367] [2] 10240 \(\Gamma_0(N)\)-optimal
14784.w5 14784br6 [0, -1, 0, 1983, 2861793] [2] 81920  
14784.w6 14784br4 [0, -1, 0, 8063, -197087] [2] 40960  

Rank

sage: E.rank()
 

The elliptic curves in class 14784.w have rank \(0\).

Modular form 14784.2.a.w

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} - q^{7} + q^{9} - q^{11} - 6q^{13} - 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.