Properties

Label 21160c
Number of curves 4
Conductor 21160
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("21160.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 21160c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21160.e3 21160c1 [0, 0, 0, -1058, -12167] [2] 12320 \(\Gamma_0(N)\)-optimal
21160.e2 21160c2 [0, 0, 0, -3703, 73002] [2, 2] 24640  
21160.e4 21160c3 [0, 0, 0, 6877, 413678] [2] 49280  
21160.e1 21160c4 [0, 0, 0, -56603, 5183142] [2] 49280  

Rank

sage: E.rank()
 

The elliptic curves in class 21160c have rank \(0\).

Modular form 21160.2.a.e

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 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.