Properties

Label 9744.l
Number of curves $6$
Conductor $9744$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9744.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9744.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9744.l1 9744q3 [0, 1, 0, -3273984, -2281239180] [2] 98304  
9744.l2 9744q5 [0, 1, 0, -679504, 175033940] [4] 196608  
9744.l3 9744q4 [0, 1, 0, -208544, -34260684] [2, 4] 98304  
9744.l4 9744q2 [0, 1, 0, -204624, -35695404] [2, 2] 49152  
9744.l5 9744q1 [0, 1, 0, -12544, -583180] [2] 24576 \(\Gamma_0(N)\)-optimal
9744.l6 9744q6 [0, 1, 0, 199696, -151670508] [4] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 9744.l have rank \(0\).

Modular form 9744.2.a.l

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} - q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.