Properties

Label 141120lj
Number of curves 8
Conductor 141120
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("141120.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120lj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.bd7 141120lj1 [0, 0, 0, 5926452, 4184495728] [2] 9437184 \(\Gamma_0(N)\)-optimal
141120.bd6 141120lj2 [0, 0, 0, -30200268, 37464430192] [2, 2] 18874368  
141120.bd4 141120lj3 [0, 0, 0, -425336268, 3375415303792] [2] 37748736  
141120.bd5 141120lj4 [0, 0, 0, -213091788, -1170570637712] [2, 2] 37748736  
141120.bd8 141120lj5 [0, 0, 0, 35843892, -3741877063568] [2] 75497472  
141120.bd2 141120lj6 [0, 0, 0, -3388291788, -75913508557712] [2, 2] 75497472  
141120.bd3 141120lj7 [0, 0, 0, -3367123788, -76908836384912] [2] 150994944  
141120.bd1 141120lj8 [0, 0, 0, -54212659788, -4858466207610512] [2] 150994944  

Rank

sage: E.rank()
 

The elliptic curves in class 141120lj have rank \(1\).

Modular form 141120.2.a.bd

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.