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Properties

Label 32490.bx
Number of curves $4$
Conductor $32490$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 32490.bx have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 32490.bx do not have complex multiplication.

Modular form 32490.2.a.bx

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} - 6 q^{11} + 4 q^{13} + 2 q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 32490.bx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bx1 32490ca4 \([1, -1, 1, -1505037587, 14350715815299]\) \(10993009831928446009969/3767761230468750000\) \(129220824287598815917968750000\) \([2]\) \(49766400\) \(4.2879\)  
32490.bx2 32490ca2 \([1, -1, 1, -1348305827, 19056290756451]\) \(7903870428425797297009/886464000000\) \(30402565814137536000000\) \([2]\) \(16588800\) \(3.7386\)  
32490.bx3 32490ca1 \([1, -1, 1, -84054947, 299359000419]\) \(-1914980734749238129/20440940544000\) \(-701051639087241363456000\) \([2]\) \(8294400\) \(3.3920\) \(\Gamma_0(N)\)-optimal
32490.bx4 32490ca3 \([1, -1, 1, 277753693, 1558118706531]\) \(69096190760262356111/70568821500000000\) \(-2420259863998847053500000000\) \([2]\) \(24883200\) \(3.9413\)