Properties

Label 95550ej
Number of curves 8
Conductor 95550
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("95550.ew1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 95550ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95550.ew7 95550ej1 [1, 0, 1, -31513151, -67728008302] [2] 10616832 \(\Gamma_0(N)\)-optimal
95550.ew6 95550ej2 [1, 0, 1, -50721151, 24585639698] [2, 2] 21233664  
95550.ew5 95550ej3 [1, 0, 1, -194683151, 999977091698] [2] 31850496  
95550.ew8 95550ej4 [1, 0, 1, 199325849, 195117693698] [2] 42467328  
95550.ew4 95550ej5 [1, 0, 1, -608096151, 5762203889698] [2] 42467328  
95550.ew2 95550ej6 [1, 0, 1, -3077083651, 65698338714698] [2, 2] 63700992  
95550.ew3 95550ej7 [1, 0, 1, -3039267901, 67391803631198] [2] 127401984  
95550.ew1 95550ej8 [1, 0, 1, -49233307401, 4204711547272198] [2] 127401984  

Rank

sage: E.rank()
 

The elliptic curves in class 95550ej have rank \(0\).

Modular form 95550.2.a.ew

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} + q^{13} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.