Properties

Label 171600bs
Number of curves $6$
Conductor $171600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("171600.ge1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 171600bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
171600.ge5 171600bs1 [0, 1, 0, -9608, -523212] [2] 524288 \(\Gamma_0(N)\)-optimal
171600.ge4 171600bs2 [0, 1, 0, -171608, -27415212] [2, 2] 1048576  
171600.ge3 171600bs3 [0, 1, 0, -189608, -21331212] [2, 2] 2097152  
171600.ge1 171600bs4 [0, 1, 0, -2745608, -1751995212] [2] 2097152  
171600.ge2 171600bs5 [0, 1, 0, -1203608, 491752788] [2] 4194304  
171600.ge6 171600bs6 [0, 1, 0, 536392, -144751212] [2] 4194304  

Rank

sage: E.rank()
 

The elliptic curves in class 171600bs have rank \(0\).

Modular form 171600.2.a.ge

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + q^{11} - q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.