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Properties

Label 55440v
Number of curves $6$
Conductor $55440$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("v1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 55440v have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1 + T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 8 T + 19 T^{2}\) 1.19.i
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 55440v do not have complex multiplication.

Modular form 55440.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 55440v

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.ce5 55440v1 \([0, 0, 0, -579738, 166831103]\) \(1847444944806639616/38285567941005\) \(446562864463882320\) \([2]\) \(589824\) \(2.1769\) \(\Gamma_0(N)\)-optimal
55440.ce4 55440v2 \([0, 0, 0, -1238583, -282369418]\) \(1125982298608534096/467044181552025\) \(87161653337965113600\) \([2, 2]\) \(1179648\) \(2.5234\)  
55440.ce6 55440v3 \([0, 0, 0, 4097517, -2067828478]\) \(10191978981888338876/8372623608979245\) \(-6250130033608570475520\) \([2]\) \(2359296\) \(2.8700\)  
55440.ce2 55440v4 \([0, 0, 0, -17116203, -27245743702]\) \(742879737792994384804/317817082130625\) \(237249180542183040000\) \([2, 2]\) \(2359296\) \(2.8700\)  
55440.ce3 55440v5 \([0, 0, 0, -14443203, -36043655902]\) \(-223180773010681046402/246754509479287425\) \(-368402508616500291225600\) \([2]\) \(4718592\) \(3.2166\)  
55440.ce1 55440v6 \([0, 0, 0, -273831123, -1744103785678]\) \(1520949008089505953959842/278553515625\) \(415878170400000000\) \([2]\) \(4718592\) \(3.2166\)