Properties

Label 141120dr
Number of curves 4
Conductor 141120
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("141120.dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.dm3 141120dr1 [0, 0, 0, -71148, -6920368] [2] 786432 \(\Gamma_0(N)\)-optimal
141120.dm2 141120dr2 [0, 0, 0, -212268, 29037008] [2, 2] 1572864  
141120.dm1 141120dr3 [0, 0, 0, -3175788, 2178181712] [2] 3145728  
141120.dm4 141120dr4 [0, 0, 0, 493332, 181164368] [2] 3145728  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.dm

sage: E.q_eigenform(10)
 
\( q - q^{5} - 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20}) \)

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.