Properties

Label 9408.cc
Number of curves $6$
Conductor $9408$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9408.cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.cc1 9408cz5 [0, 1, 0, -75329, -7982913] [2] 24576  
9408.cc2 9408cz4 [0, 1, 0, -12609, 540735] [2] 12288  
9408.cc3 9408cz3 [0, 1, 0, -4769, -122529] [2, 2] 12288  
9408.cc4 9408cz2 [0, 1, 0, -849, 6831] [2, 2] 6144  
9408.cc5 9408cz1 [0, 1, 0, 131, 755] [2] 3072 \(\Gamma_0(N)\)-optimal
9408.cc6 9408cz6 [0, 1, 0, 3071, -478465] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 9408.cc have rank \(0\).

Modular form 9408.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.