Properties

Label 9792.y
Number of curves 4
Conductor 9792
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9792.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9792.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9792.y1 9792v4 [0, 0, 0, -65100, 4417904] [2] 55296  
9792.y2 9792v3 [0, 0, 0, -59340, 5562992] [2] 27648  
9792.y3 9792v2 [0, 0, 0, -24780, -1501072] [2] 18432  
9792.y4 9792v1 [0, 0, 0, -1740, -17296] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9792.y have rank \(1\).

Modular form 9792.2.a.y

sage: E.q_eigenform(10)
 
\( q - 4q^{7} + 6q^{11} - 2q^{13} + q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.