Properties

Label 38720q
Number of curves 4
Conductor 38720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38720.da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38720q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.da4 38720q1 [0, -1, 0, -21941, -1217995] [2] 138240 \(\Gamma_0(N)\)-optimal
38720.da3 38720q2 [0, -1, 0, -48561, 2343761] [2] 276480  
38720.da2 38720q3 [0, -1, 0, -215541, 38102165] [2] 414720  
38720.da1 38720q4 [0, -1, 0, -3436561, 2453222961] [2] 829440  

Rank

sage: E.rank()
 

The elliptic curves in class 38720q have rank \(0\).

Modular form 38720.2.a.da

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + 4q^{7} + q^{9} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.