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Properties

Label 262080.kx
Number of curves $3$
Conductor $262080$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("kx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 262080.kx have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 3 T + 11 T^{2}\) 1.11.d
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 9 T + 23 T^{2}\) 1.23.j
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 262080.kx do not have complex multiplication.

Modular form 262080.2.a.kx

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + q^{7} - 3 q^{11} - q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 262080.kx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
262080.kx1 262080kx3 \([0, 0, 0, -29089841772, 2025265927753136]\) \(-14245586655234650511684983641/1028175397808386133196800\) \(-196487378371166467811040873676800\) \([]\) \(1097349120\) \(4.9462\)  
262080.kx2 262080kx1 \([0, 0, 0, -333185772, -2538272778064]\) \(-21405018343206000779641/2177246093750000000\) \(-416078208000000000000000000\) \([]\) \(121927680\) \(3.8476\) \(\Gamma_0(N)\)-optimal
262080.kx3 262080kx2 \([0, 0, 0, 2051814228, 2328225221936]\) \(4998853083179567995470359/2905108466204672000000\) \(-555174873494508244303872000000\) \([]\) \(365783040\) \(4.3969\)