Properties

Label 38025bc
Number of curves 8
Conductor 38025
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("38025.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38025bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38025.cj7 38025bc1 [1, -1, 0, -792, -1381509] [2] 110592 \(\Gamma_0(N)\)-optimal
38025.cj6 38025bc2 [1, -1, 0, -190917, -31611384] [2, 2] 221184  
38025.cj5 38025bc3 [1, -1, 0, -381042, 41966991] [2, 2] 442368  
38025.cj4 38025bc4 [1, -1, 0, -3042792, -2042183259] [2] 442368  
38025.cj8 38025bc5 [1, -1, 0, 1330083, 314035866] [2] 884736  
38025.cj2 38025bc6 [1, -1, 0, -5134167, 4476632616] [2, 2] 884736  
38025.cj3 38025bc7 [1, -1, 0, -4183542, 6184905741] [2] 1769472  
38025.cj1 38025bc8 [1, -1, 0, -82134792, 286529921991] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 38025bc have rank \(0\).

Modular form 38025.2.a.cj

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 3q^{8} - 4q^{11} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.