Properties

Label 97461.q
Number of curves $6$
Conductor $97461$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("97461.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.q1 97461m6 [1, -1, 0, -8896743, -10210176684] [2] 3145728  
97461.q2 97461m4 [1, -1, 0, -612558, -125009865] [2, 2] 1572864  
97461.q3 97461m2 [1, -1, 0, -239913, 43798320] [2, 2] 786432  
97461.q4 97461m1 [1, -1, 0, -237708, 44667531] [2] 393216 \(\Gamma_0(N)\)-optimal
97461.q5 97461m3 [1, -1, 0, 97452, 156950541] [2] 1572864  
97461.q6 97461m5 [1, -1, 0, 1709307, -848038626] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 97461.q have rank \(0\).

Modular form 97461.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} - 4q^{11} - q^{13} - q^{16} + q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.