Properties

Label 98736.n
Number of curves 6
Conductor 98736
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("98736.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 98736.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98736.n1 98736bz6 [0, -1, 0, -53712424, -151498706192] [2] 3932160  
98736.n2 98736bz4 [0, -1, 0, -3357064, -2366272016] [2, 2] 1966080  
98736.n3 98736bz5 [0, -1, 0, -3182824, -2623032080] [2] 3932160  
98736.n4 98736bz2 [0, -1, 0, -220744, -32849936] [2, 2] 983040  
98736.n5 98736bz1 [0, -1, 0, -65864, 6055920] [2] 491520 \(\Gamma_0(N)\)-optimal
98736.n6 98736bz3 [0, -1, 0, 437496, -191880720] [2] 1966080  

Rank

sage: E.rank()
 

The elliptic curves in class 98736.n have rank \(1\).

Modular form 98736.2.a.n

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.