Properties

Label 9792k
Number of curves 6
Conductor 9792
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9792.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9792k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9792.k5 9792k1 [0, 0, 0, -19596, -979216] [2] 24576 \(\Gamma_0(N)\)-optimal
9792.k4 9792k2 [0, 0, 0, -65676, 5342960] [2, 2] 49152  
9792.k2 9792k3 [0, 0, 0, -998796, 384189680] [2, 2] 98304  
9792.k6 9792k4 [0, 0, 0, 130164, 31115504] [2] 98304  
9792.k1 9792k5 [0, 0, 0, -15980556, 24588721136] [2] 196608  
9792.k3 9792k6 [0, 0, 0, -946956, 425848304] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 9792k have rank \(0\).

Modular form 9792.2.a.k

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

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.