Properties

Label 8190.bx
Number of curves $8$
Conductor $8190$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 8190.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8190.bx1 8190bv8 \([1, -1, 1, -20391107, 35440483331]\) \(1286229821345376481036009/247265484375000000\) \(180256538109375000000\) \([12]\) \(663552\) \(2.8872\)  
8190.bx2 8190bv7 \([1, -1, 1, -8969027, -10011937021]\) \(109454124781830273937129/3914078300576808000\) \(2853363081120493032000\) \([6]\) \(663552\) \(2.8872\)  
8190.bx3 8190bv4 \([1, -1, 1, -8890592, -10201158529]\) \(106607603143751752938169/5290068420\) \(3856459878180\) \([2]\) \(221184\) \(2.3379\)  
8190.bx4 8190bv6 \([1, -1, 1, -1409027, 429934979]\) \(424378956393532177129/136231857216000000\) \(99313023910464000000\) \([2, 6]\) \(331776\) \(2.5407\)  
8190.bx5 8190bv5 \([1, -1, 1, -618872, -120756481]\) \(35958207000163259449/12145729518877500\) \(8854236819261697500\) \([4]\) \(221184\) \(2.3379\)  
8190.bx6 8190bv2 \([1, -1, 1, -555692, -159271009]\) \(26031421522845051769/5797789779600\) \(4226588749328400\) \([2, 2]\) \(110592\) \(1.9914\)  
8190.bx7 8190bv1 \([1, -1, 1, -30812, -3066721]\) \(-4437543642183289/3033210136320\) \(-2211210189377280\) \([2]\) \(55296\) \(1.6448\) \(\Gamma_0(N)\)-optimal
8190.bx8 8190bv3 \([1, -1, 1, 249853, 45738371]\) \(2366200373628880151/2612420149248000\) \(-1904454288801792000\) \([6]\) \(165888\) \(2.1941\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 8190.bx do not have complex multiplication.

Modular form 8190.2.a.bx

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

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.