Properties

Label 187590.g
Number of curves $6$
Conductor $187590$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("187590.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187590.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187590.g1 187590ct3 [1, 1, 0, -57629848, 168367163008] [2] 15925248  
187590.g2 187590ct6 [1, 1, 0, -51228128, -140535029448] [2] 31850496  
187590.g3 187590ct4 [1, 1, 0, -4955928, 474872832] [2, 2] 15925248  
187590.g4 187590ct2 [1, 1, 0, -3603928, 2626445632] [2, 2] 7962624  
187590.g5 187590ct1 [1, 1, 0, -142808, 71446848] [2] 3981312 \(\Gamma_0(N)\)-optimal
187590.g6 187590ct5 [1, 1, 0, 19684272, 3811155912] [2] 31850496  

Rank

sage: E.rank()
 

The elliptic curves in class 187590.g have rank \(1\).

Modular form 187590.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.