Properties

Label 92400.q
Number of curves $6$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("92400.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.q1 92400dk6 [0, -1, 0, -5300008, 4697918512] [2] 3145728  
92400.q2 92400dk4 [0, -1, 0, -350008, 64718512] [2, 2] 1572864  
92400.q3 92400dk2 [0, -1, 0, -108008, -12721488] [2, 2] 786432  
92400.q4 92400dk1 [0, -1, 0, -106008, -13249488] [2] 393216 \(\Gamma_0(N)\)-optimal
92400.q5 92400dk3 [0, -1, 0, 101992, -56401488] [2] 1572864  
92400.q6 92400dk5 [0, -1, 0, 727992, 383806512] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.q have rank \(0\).

Modular form 92400.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{7} + q^{9} - q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.