Properties

Label 219849.u
Number of curves $6$
Conductor $219849$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("219849.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 219849.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
219849.u1 219849p4 [1, 0, 1, -73869272, -244373876341] [2] 10616832  
219849.u2 219849p5 [1, 0, 1, -15331317, 18781712509] [2] 21233664  
219849.u3 219849p3 [1, 0, 1, -4705282, -3664723825] [2, 2] 10616832  
219849.u4 219849p2 [1, 0, 1, -4616837, -3818618125] [2, 2] 5308416  
219849.u5 219849p1 [1, 0, 1, -283032, -62075951] [2] 2654208 \(\Gamma_0(N)\)-optimal
219849.u6 219849p6 [1, 0, 1, 4505633, -16261571179] [2] 21233664  

Rank

sage: E.rank()
 

The elliptic curves in class 219849.u have rank \(0\).

Modular form 219849.2.a.u

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} + 2q^{13} + q^{14} - 2q^{15} - q^{16} + 2q^{17} + q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.