Properties

Label 82810.q
Number of curves $4$
Conductor $82810$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("82810.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 82810.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
82810.q1 82810e4 [1, -1, 0, -2216720, 1270815846] [2] 1474560  
82810.q2 82810e3 [1, -1, 0, -726140, -222380950] [2] 1474560  
82810.q3 82810e2 [1, -1, 0, -146470, 17486496] [2, 2] 737280  
82810.q4 82810e1 [1, -1, 0, 19150, 1620100] [2] 368640 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 82810.q have rank \(0\).

Modular form 82810.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} - 3q^{9} + q^{10} - 4q^{11} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.