Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("38720.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38720dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.p3 38720dn1 [0, 1, 0, -645, 4123] [2] 23040 \(\Gamma_0(N)\)-optimal
38720.p4 38720dn2 [0, 1, 0, 1775, 29775] [2] 46080  
38720.p1 38720dn3 [0, 1, 0, -20005, -1095525] [2] 69120  
38720.p2 38720dn4 [0, 1, 0, -17585, -1368017] [2] 138240  

Rank

sage: E.rank()
 

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

Modular form 38720.2.a.p

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 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.