Properties

Label 185130bf
Number of curves 6
Conductor 185130
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("185130.dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 185130bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.dp4 185130bf1 [1, -1, 1, -7960613, 8647031517] [2] 5898240 \(\Gamma_0(N)\)-optimal
185130.dp3 185130bf2 [1, -1, 1, -8047733, 8448153981] [2, 2] 11796480  
185130.dp5 185130bf3 [1, -1, 1, 4170847, 31824741237] [2] 23592960  
185130.dp2 185130bf4 [1, -1, 1, -21660233, -27657641019] [2, 2] 23592960  
185130.dp6 185130bf5 [1, -1, 1, 57020017, -182468900919] [2] 47185920  
185130.dp1 185130bf6 [1, -1, 1, -318140483, -2183780611119] [2] 47185920  

Rank

sage: E.rank()
 

The elliptic curves in class 185130bf have rank \(1\).

Modular form 185130.2.a.dp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 6q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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 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.