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Properties

Label 14784.ci
Number of curves $6$
Conductor $14784$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ci1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 14784.ci have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 14784.ci do not have complex multiplication.

Modular form 14784.2.a.ci

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{7} + q^{9} - q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 14784.ci

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.ci1 14784cl5 \([0, 1, 0, -189057, 31547007]\) \(5701568801608514/6277868289\) \(822852752375808\) \([4]\) \(98304\) \(1.7769\)  
14784.ci2 14784cl3 \([0, 1, 0, -14817, 218655]\) \(5489767279588/2847396321\) \(186606965293056\) \([2, 2]\) \(49152\) \(1.4303\)  
14784.ci3 14784cl2 \([0, 1, 0, -8337, -293265]\) \(3911877700432/38900169\) \(637340368896\) \([2, 2]\) \(24576\) \(1.0837\)  
14784.ci4 14784cl1 \([0, 1, 0, -8317, -294733]\) \(62140690757632/6237\) \(6386688\) \([2]\) \(12288\) \(0.73716\) \(\Gamma_0(N)\)-optimal
14784.ci5 14784cl4 \([0, 1, 0, -2177, -710913]\) \(-17418812548/3314597517\) \(-217225462874112\) \([2]\) \(49152\) \(1.4303\)  
14784.ci6 14784cl6 \([0, 1, 0, 55743, 1756863]\) \(146142660369886/94532266521\) \(-12390533237440512\) \([2]\) \(98304\) \(1.7769\)