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Properties

Label 2640.t
Number of curves $6$
Conductor $2640$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 2640.t have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 2640.t do not have complex multiplication.

Modular form 2640.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - q^{11} + 6 q^{13} + q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 2640.t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2640.t1 2640v5 \([0, 1, 0, -2737360, 1742282900]\) \(553808571467029327441/12529687500\) \(51321600000000\) \([4]\) \(36864\) \(2.1549\)  
2640.t2 2640v3 \([0, 1, 0, -189200, -31669740]\) \(182864522286982801/463015182960\) \(1896510189404160\) \([2]\) \(18432\) \(1.8083\)  
2640.t3 2640v4 \([0, 1, 0, -171280, 27115028]\) \(135670761487282321/643043610000\) \(2633906626560000\) \([2, 4]\) \(18432\) \(1.8083\)  
2640.t4 2640v6 \([0, 1, 0, -83280, 55028628]\) \(-15595206456730321/310672490129100\) \(-1272514519568793600\) \([4]\) \(36864\) \(2.1549\)  
2640.t5 2640v2 \([0, 1, 0, -16400, -81900]\) \(119102750067601/68309049600\) \(279793867161600\) \([2, 2]\) \(9216\) \(1.4618\)  
2640.t6 2640v1 \([0, 1, 0, 4080, -8172]\) \(1833318007919/1070530560\) \(-4384893173760\) \([2]\) \(4608\) \(1.1152\) \(\Gamma_0(N)\)-optimal