Properties

Label 8190m
Number of curves 8
Conductor 8190
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("8190.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8190m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8190.h7 8190m1 [1, -1, 0, -231525, -42591339] [2] 73728 \(\Gamma_0(N)\)-optimal
8190.h6 8190m2 [1, -1, 0, -372645, 15578325] [2, 2] 147456  
8190.h5 8190m3 [1, -1, 0, -1430325, 630090981] [6] 221184  
8190.h4 8190m4 [1, -1, 0, -4467645, 3629825325] [2] 294912  
8190.h8 8190m5 [1, -1, 0, 1464435, 122496381] [2] 294912  
8190.h2 8190m6 [1, -1, 0, -22607145, 41378528025] [2, 6] 442368  
8190.h1 8190m7 [1, -1, 0, -361714095, 2647958009895] [6] 884736  
8190.h3 8190m8 [1, -1, 0, -22329315, 42444895131] [6] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 8190m have rank \(0\).

Modular form 8190.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + q^{13} - q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.