Properties

Label 37845.d
Number of curves 8
Conductor 37845
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("37845.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37845.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37845.d1 37845d8 [1, -1, 1, -16349198, 25448520512] [2] 802816  
37845.d2 37845d6 [1, -1, 1, -1021973, 397703972] [2, 2] 401408  
37845.d3 37845d7 [1, -1, 1, -832748, 549386732] [2] 802816  
37845.d4 37845d4 [1, -1, 1, -605678, -181279114] [2] 200704  
37845.d5 37845d3 [1, -1, 1, -75848, 3737522] [2, 2] 200704  
37845.d6 37845d2 [1, -1, 1, -38003, -2802094] [2, 2] 100352  
37845.d7 37845d1 [1, -1, 1, -158, -122668] [2] 50176 \(\Gamma_0(N)\)-optimal
37845.d8 37845d5 [1, -1, 1, 264757, 27852356] [2] 401408  

Rank

sage: E.rank()
 

The elliptic curves in class 37845.d have rank \(0\).

Modular form 37845.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - q^{5} + 3q^{8} + q^{10} - 4q^{11} - 2q^{13} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.