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Properties

Label 293046.cu
Number of curves $4$
Conductor $293046$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 293046.cu have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(13\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 293046.cu do not have complex multiplication.

Modular form 293046.2.a.cu

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} + 2 q^{10} + q^{12} + 2 q^{14} + 2 q^{15} + q^{16} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 293046.cu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
293046.cu1 293046cu4 \([1, 0, 0, -1030277492, -12360359398050]\) \(211293405175481/6973568802\) \(3991677962018377638834138546\) \([2]\) \(208896000\) \(4.0693\)  
293046.cu2 293046cu3 \([1, 0, 0, -1021974522, -12575079184032]\) \(206226044828441/236196\) \(135198833579514560410308\) \([2]\) \(104448000\) \(3.7228\)  
293046.cu3 293046cu2 \([1, 0, 0, -141859702, 650319865220]\) \(551569744601/2592\) \(1483663468636648125216\) \([2]\) \(41779200\) \(3.2646\)  
293046.cu4 293046cu1 \([1, 0, 0, -9012182, 9808832292]\) \(141420761/9216\) \(5275247888485860000768\) \([2]\) \(20889600\) \(2.9180\) \(\Gamma_0(N)\)-optimal