Properties

Label 38440.g
Number of curves 4
Conductor 38440
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38440.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38440.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38440.g1 38440e4 [0, 0, 0, -102827, 12690966] [2] 115200  
38440.g2 38440e2 [0, 0, 0, -6727, 178746] [2, 2] 57600  
38440.g3 38440e1 [0, 0, 0, -1922, -29791] [2] 28800 \(\Gamma_0(N)\)-optimal
38440.g4 38440e3 [0, 0, 0, 12493, 1012894] [2] 115200  

Rank

sage: E.rank()
 

The elliptic curves in class 38440.g have rank \(1\).

Modular form 38440.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{7} - 3q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.