Properties

Label 37905k
Number of curves 4
Conductor 37905
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("37905.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37905k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37905.g3 37905k1 [1, 1, 1, -910, -10390] [2] 24192 \(\Gamma_0(N)\)-optimal
37905.g2 37905k2 [1, 1, 1, -2715, 40872] [2, 2] 48384  
37905.g4 37905k3 [1, 1, 1, 6310, 264692] [2] 96768  
37905.g1 37905k4 [1, 1, 1, -40620, 3133920] [2] 96768  

Rank

sage: E.rank()
 

The elliptic curves in class 37905k have rank \(0\).

Modular form 37905.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + q^{7} + 3q^{8} + q^{9} - q^{10} + q^{12} + 6q^{13} - q^{14} - q^{15} - q^{16} + 2q^{17} - q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.