Properties

Label 235200.qr
Number of curves 8
Conductor 235200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.qr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200.qr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.qr1 235200qr8 [0, 1, 0, -150590721633, -22492949306215137] [2] 452984832  
235200.qr2 235200qr6 [0, 1, 0, -9411921633, -351454565815137] [2, 2] 226492416  
235200.qr3 235200qr7 [0, 1, 0, -9353121633, -356062545415137] [2] 452984832  
235200.qr4 235200qr3 [0, 1, 0, -1181489633, 15626528872863] [2] 113246208  
235200.qr5 235200qr4 [0, 1, 0, -591921633, -5419505815137] [2, 2] 113246208  
235200.qr6 235200qr2 [0, 1, 0, -83889633, 173418472863] [2, 2] 56623104  
235200.qr7 235200qr1 [0, 1, 0, 16462367, 19378152863] [2] 28311552 \(\Gamma_0(N)\)-optimal
235200.qr8 235200qr5 [0, 1, 0, 99566367, -17323471735137] [2] 226492416  

Rank

sage: E.rank()
 

The elliptic curves in class 235200.qr have rank \(0\).

Modular form 235200.2.a.qr

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} - 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.