Properties

Label 6720cd
Number of curves 8
Conductor 6720
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("6720.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.bq7 6720cd1 [0, 1, 0, 13439, -447361] [2] 24576 \(\Gamma_0(N)\)-optimal
6720.bq6 6720cd2 [0, 1, 0, -68481, -4068225] [2, 2] 49152  
6720.bq4 6720cd3 [0, 1, 0, -964481, -364797825] [2] 98304  
6720.bq5 6720cd4 [0, 1, 0, -483201, 126236799] [2, 2] 98304  
6720.bq2 6720cd5 [0, 1, 0, -7683201, 8194556799] [2, 2] 196608  
6720.bq8 6720cd6 [0, 1, 0, 81279, 404073855] [2] 196608  
6720.bq1 6720cd7 [0, 1, 0, -122931201, 524574745599] [2] 393216  
6720.bq3 6720cd8 [0, 1, 0, -7635201, 8302047999] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 6720cd have rank \(0\).

Modular form 6720.2.a.bq

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.