Properties

Label 82800.dl
Number of curves $6$
Conductor $82800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("82800.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 82800.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
82800.dl1 82800du4 [0, 0, 0, -397440075, 3049689312250] [2] 7077888  
82800.dl2 82800du6 [0, 0, 0, -92988075, -295638659750] [2] 14155776  
82800.dl3 82800du3 [0, 0, 0, -25488075, 45033840250] [2, 2] 7077888  
82800.dl4 82800du2 [0, 0, 0, -24840075, 47651112250] [2, 2] 3538944  
82800.dl5 82800du1 [0, 0, 0, -1512075, 785160250] [2] 1769472 \(\Gamma_0(N)\)-optimal
82800.dl6 82800du5 [0, 0, 0, 31643925, 218200932250] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 82800.dl have rank \(0\).

Modular form 82800.2.a.dl

sage: E.q_eigenform(10)
 
\( q + 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.