Properties

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

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

Elliptic curves in class 9792.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9792.y1 9792v4 \([0, 0, 0, -65100, 4417904]\) \(159661140625/48275138\) \(9225522538610688\) \([2]\) \(55296\) \(1.7685\)  
9792.y2 9792v3 \([0, 0, 0, -59340, 5562992]\) \(120920208625/19652\) \(3755555684352\) \([2]\) \(27648\) \(1.4219\)  
9792.y3 9792v2 \([0, 0, 0, -24780, -1501072]\) \(8805624625/2312\) \(441830080512\) \([2]\) \(18432\) \(1.2192\)  
9792.y4 9792v1 \([0, 0, 0, -1740, -17296]\) \(3048625/1088\) \(207920037888\) \([2]\) \(9216\) \(0.87263\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 9792.y do not have complex multiplication.

Modular form 9792.2.a.y

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

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.