Properties

Label 141120.bb
Number of curves $6$
Conductor $141120$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("141120.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.bb1 141120dd5 [0, 0, 0, -474163788, 3974117369488] [2] 18874368  
141120.bb2 141120dd3 [0, 0, 0, -29635788, 62093158288] [2, 2] 9437184  
141120.bb3 141120dd6 [0, 0, 0, -27660108, 70728460432] [2] 18874368  
141120.bb4 141120dd4 [0, 0, 0, -10443468, -12277759088] [2] 9437184  
141120.bb5 141120dd2 [0, 0, 0, -1976268, 832853392] [2, 2] 4718592  
141120.bb6 141120dd1 [0, 0, 0, 281652, 80514448] [2] 2359296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141120.bb have rank \(0\).

Modular form 141120.2.a.bb

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.