Properties

Label 279174.cr
Number of curves $6$
Conductor $279174$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("279174.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 279174.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
279174.cr1 279174cr6 [1, 0, 0, -22869732, -42097375692] [2] 18874368  
279174.cr2 279174cr3 [1, 0, 0, -5119352, 4457767248] [2] 9437184  
279174.cr3 279174cr4 [1, 0, 0, -1466392, -621983440] [2, 2] 9437184  
279174.cr4 279174cr2 [1, 0, 0, -333512, 63408960] [2, 2] 4718592  
279174.cr5 279174cr1 [1, 0, 0, 36408, 5479488] [2] 2359296 \(\Gamma_0(N)\)-optimal
279174.cr6 279174cr5 [1, 0, 0, 1810868, -3007173268] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 279174.cr have rank \(0\).

Modular form 279174.2.a.cr

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} - 2q^{13} - q^{14} + 2q^{15} + q^{16} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.