Properties

Label 45486bh
Number of curves $6$
Conductor $45486$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("45486.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 45486bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
45486.bl5 45486bh1 [1, -1, 1, -13064, 1272395] [2] 221184 \(\Gamma_0(N)\)-optimal
45486.bl4 45486bh2 [1, -1, 1, -272984, 54919883] [2, 2] 442368  
45486.bl3 45486bh3 [1, -1, 1, -337964, 26848523] [2, 2] 884736  
45486.bl1 45486bh4 [1, -1, 1, -4366724, 3513311435] [2] 884736  
45486.bl6 45486bh5 [1, -1, 1, 1254046, 206427251] [2] 1769472  
45486.bl2 45486bh6 [1, -1, 1, -2969654, -1950077005] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 45486bh have rank \(0\).

Modular form 45486.2.a.bl

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} + 2q^{10} + 4q^{11} - 6q^{13} - q^{14} + q^{16} - 2q^{17} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.