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Properties

Label 29040ch
Number of curves $8$
Conductor $29040$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ch1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 29040ch have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29040ch do not have complex multiplication.

Modular form 29040.2.a.ch

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} - 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 29040ch

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29040.b8 29040ch1 \([0, -1, 0, 2864, 180160]\) \(357911/2160\) \(-15673637928960\) \([2]\) \(69120\) \(1.2138\) \(\Gamma_0(N)\)-optimal
29040.b6 29040ch2 \([0, -1, 0, -35856, 2379456]\) \(702595369/72900\) \(528985280102400\) \([2, 2]\) \(138240\) \(1.5604\)  
29040.b7 29040ch3 \([0, -1, 0, -26176, -5325824]\) \(-273359449/1536000\) \(-11145698082816000\) \([2]\) \(207360\) \(1.7631\)  
29040.b5 29040ch4 \([0, -1, 0, -132656, -15973824]\) \(35578826569/5314410\) \(38563026919464960\) \([2]\) \(276480\) \(1.9070\)  
29040.b4 29040ch5 \([0, -1, 0, -558576, 160868160]\) \(2656166199049/33750\) \(244900592640000\) \([2]\) \(276480\) \(1.9070\)  
29040.b3 29040ch6 \([0, -1, 0, -645696, -199111680]\) \(4102915888729/9000000\) \(65306824704000000\) \([2, 2]\) \(414720\) \(2.1097\)  
29040.b1 29040ch7 \([0, -1, 0, -10325696, -12767623680]\) \(16778985534208729/81000\) \(587761422336000\) \([2]\) \(829440\) \(2.4563\)  
29040.b2 29040ch8 \([0, -1, 0, -878016, -42806784]\) \(10316097499609/5859375000\) \(42517464000000000000\) \([2]\) \(829440\) \(2.4563\)