Properties

Label 92736.bh
Number of curves $6$
Conductor $92736$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("92736.bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92736.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92736.bh1 92736dz6 [0, 0, 0, -45581196, -118446524656] [2] 6291456  
92736.bh2 92736dz4 [0, 0, 0, -10203276, 12544284944] [2] 3145728  
92736.bh3 92736dz3 [0, 0, 0, -2922636, -1749767920] [2, 2] 3145728  
92736.bh4 92736dz2 [0, 0, 0, -664716, 178495760] [2, 2] 1572864  
92736.bh5 92736dz1 [0, 0, 0, 72564, 15409424] [2] 786432 \(\Gamma_0(N)\)-optimal
92736.bh6 92736dz5 [0, 0, 0, 3609204, -8461886704] [2] 6291456  

Rank

sage: E.rank()
 

The elliptic curves in class 92736.bh have rank \(1\).

Modular form 92736.2.a.bh

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - q^{7} + 4q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.