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Properties

Label 283920.ge
Number of curves $6$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ge1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 283920.ge have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 283920.ge do not have complex multiplication.

Modular form 283920.2.a.ge

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 283920.ge

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.ge1 283920ge5 \([0, 1, 0, -369569256, 2734290414324]\) \(282352188585428161201/20813369346315\) \(411493001138656701788160\) \([2]\) \(66060288\) \(3.5815\)  
283920.ge2 283920ge4 \([0, 1, 0, -126682456, -548851142956]\) \(11372424889583066401/50586128775\) \(1000118606423363481600\) \([2]\) \(33030144\) \(3.2349\)  
283920.ge3 283920ge3 \([0, 1, 0, -24606456, 36819303444]\) \(83339496416030401/18593645841225\) \(367607714157516394598400\) \([2, 2]\) \(33030144\) \(3.2349\)  
283920.ge4 283920ge2 \([0, 1, 0, -8044456, -8288959756]\) \(2912015927948401/184878500625\) \(3655160671122455040000\) \([2, 2]\) \(16515072\) \(2.8883\)  
283920.ge5 283920ge1 \([0, 1, 0, 405544, -545379756]\) \(373092501599/6718359375\) \(-132826060785600000000\) \([2]\) \(8257536\) \(2.5418\) \(\Gamma_0(N)\)-optimal
283920.ge6 283920ge6 \([0, 1, 0, 55364344, 226542029364]\) \(949279533867428399/1670570708285115\) \(-33028201389617019486351360\) \([2]\) \(66060288\) \(3.5815\)