Properties

Label 38720.dd
Number of curves 4
Conductor 38720
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("38720.dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38720.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.dd1 38720bm3 [0, -1, 0, -20005, 1095525] [2] 69120  
38720.dd2 38720bm4 [0, -1, 0, -17585, 1368017] [2] 138240  
38720.dd3 38720bm1 [0, -1, 0, -645, -4123] [2] 23040 \(\Gamma_0(N)\)-optimal
38720.dd4 38720bm2 [0, -1, 0, 1775, -29775] [2] 46080  

Rank

sage: E.rank()
 

The elliptic curves in class 38720.dd have rank \(1\).

Modular form 38720.2.a.dd

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 LMFDB 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 LMFDB labels.