Properties

Label 187425.bl
Number of curves 4
Conductor 187425
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("187425.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187425.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187425.bl1 187425bh3 [1, -1, 1, -18588380, 30850145372] [2] 9437184  
187425.bl2 187425bh4 [1, -1, 1, -5909630, -5138762128] [2] 9437184  
187425.bl3 187425bh2 [1, -1, 1, -1224005, 427760372] [2, 2] 4718592  
187425.bl4 187425bh1 [1, -1, 1, 154120, 39129122] [2] 2359296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187425.bl have rank \(2\).

Modular form 187425.2.a.bl

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 3q^{8} - 6q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.