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Properties

Label 141120.gv
Number of curves $6$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 141120.gv have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 141120.gv do not have complex multiplication.

Modular form 141120.2.a.gv

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 141120.gv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.gv1 141120mu6 \([0, 0, 0, -474163788, -3974117369488]\) \(524388516989299201/3150\) \(70821683173785600\) \([2]\) \(18874368\) \(3.2987\)  
141120.gv2 141120mu4 \([0, 0, 0, -29635788, -62093158288]\) \(128031684631201/9922500\) \(223088301997424640000\) \([2, 2]\) \(9437184\) \(2.9522\)  
141120.gv3 141120mu5 \([0, 0, 0, -27660108, -70728460432]\) \(-104094944089921/35880468750\) \(-806703234901401600000000\) \([2]\) \(18874368\) \(3.2987\)  
141120.gv4 141120mu3 \([0, 0, 0, -10443468, 12277759088]\) \(5602762882081/345888060\) \(7776626856798521917440\) \([2]\) \(9437184\) \(2.9522\)  
141120.gv5 141120mu2 \([0, 0, 0, -1976268, -832853392]\) \(37966934881/8643600\) \(194334698628867686400\) \([2, 2]\) \(4718592\) \(2.6056\)  
141120.gv6 141120mu1 \([0, 0, 0, 281652, -80514448]\) \(109902239/188160\) \(-4230415208247459840\) \([2]\) \(2359296\) \(2.2590\) \(\Gamma_0(N)\)-optimal