Properties

Label 184041bm
Number of curves $6$
Conductor $184041$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("184041.bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 184041bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
184041.bn5 184041bm1 [1, -1, 0, -4420818, 5133179871] [2] 10321920 \(\Gamma_0(N)\)-optimal
184041.bn4 184041bm2 [1, -1, 0, -78957423, 270021366720] [2, 2] 20643840  
184041.bn1 184041bm3 [1, -1, 0, -1263261258, 17282072234961] [2] 41287680  
184041.bn3 184041bm4 [1, -1, 0, -87239268, 209920017555] [2, 2] 41287680  
184041.bn6 184041bm5 [1, -1, 0, 246795147, 1430281349316] [2] 82575360  
184041.bn2 184041bm6 [1, -1, 0, -553783203, -4857027042906] [2] 82575360  

Rank

sage: E.rank()
 

The elliptic curves in class 184041bm have rank \(1\).

Modular form 184041.2.a.bn

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.