Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("8190.bx1")
sage: E.isogeny_class()

Elliptic curves in class 8190.bx

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
8190.bx1 8190bv8 [1, -1, 1, -20391107, 35440483331] 12 663552  
8190.bx2 8190bv7 [1, -1, 1, -8969027, -10011937021] 6 663552  
8190.bx3 8190bv4 [1, -1, 1, -8890592, -10201158529] 2 221184  
8190.bx4 8190bv6 [1, -1, 1, -1409027, 429934979] 12 331776  
8190.bx5 8190bv5 [1, -1, 1, -618872, -120756481] 4 221184  
8190.bx6 8190bv2 [1, -1, 1, -555692, -159271009] 4 110592  
8190.bx7 8190bv1 [1, -1, 1, -30812, -3066721] 2 55296 \(\Gamma_0(N)\)-optimal
8190.bx8 8190bv3 [1, -1, 1, 249853, 45738371] 6 165888  

Rank

sage: E.rank()

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

Modular form 8190.2.a.bx

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.