Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("14784.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14784bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14784.cj4 14784bm1 [0, 1, 0, -2177, 38367] [2] 10240 \(\Gamma_0(N)\)-optimal
14784.cj3 14784bm2 [0, 1, 0, -2497, 26015] [2, 2] 20480  
14784.cj2 14784bm3 [0, 1, 0, -18177, -930465] [2, 2] 40960  
14784.cj6 14784bm4 [0, 1, 0, 8063, 197087] [2] 40960  
14784.cj1 14784bm5 [0, 1, 0, -289217, -59962977] [2] 81920  
14784.cj5 14784bm6 [0, 1, 0, 1983, -2861793] [2] 81920  

Rank

sage: E.rank()
 

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

Modular form 14784.2.a.cj

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.