Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("58800.cq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.cq7 58800fd1 [0, -1, 0, -804008, -97369488] [2] 1327104 \(\Gamma_0(N)\)-optimal
58800.cq5 58800fd2 [0, -1, 0, -7076008, 7178150512] [2, 2] 2654208  
58800.cq4 58800fd3 [0, -1, 0, -52548008, -146598745488] [2] 3981312  
58800.cq6 58800fd4 [0, -1, 0, -1588008, 18022438512] [2] 5308416  
58800.cq2 58800fd5 [0, -1, 0, -112916008, 461866790512] [2] 5308416  
58800.cq3 58800fd6 [0, -1, 0, -52940008, -144300057488] [2, 2] 7962624  
58800.cq8 58800fd7 [0, -1, 0, 14287992, -485818297488] [2] 15925248  
58800.cq1 58800fd8 [0, -1, 0, -126440008, 344327942512] [2] 15925248  

Rank

sage: E.rank()
 

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

Modular form 58800.2.a.cq

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.