Properties

Label 58800.cr
Number of curves $8$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.cr1 58800fe8 [0, -1, 0, -6884157408, -219846607634688] [2] 31850496  
58800.cr2 58800fe6 [0, -1, 0, -430269408, -3434835218688] [2, 2] 15925248  
58800.cr3 58800fe7 [0, -1, 0, -398909408, -3956791058688] [2] 31850496  
58800.cr4 58800fe5 [0, -1, 0, -85407408, -298432634688] [2] 10616832  
58800.cr5 58800fe3 [0, -1, 0, -28861408, -45346066688] [2] 7962624  
58800.cr6 58800fe2 [0, -1, 0, -11319408, 7698981312] [2, 2] 5308416  
58800.cr7 58800fe1 [0, -1, 0, -9751408, 11719333312] [2] 2654208 \(\Gamma_0(N)\)-optimal
58800.cr8 58800fe4 [0, -1, 0, 37680592, 56502981312] [2] 10616832  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.cr have rank \(1\).

Modular form 58800.2.a.cr

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.