Properties

Label 141120cb
Number of curves $4$
Conductor $141120$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ov3 141120cb1 [0, 0, 0, -99372, 7611856] [2] 1179648 \(\Gamma_0(N)\)-optimal
141120.ov2 141120cb2 [0, 0, 0, -663852, -202600496] [2, 2] 2359296  
141120.ov4 141120cb3 [0, 0, 0, 182868, -683876144] [2] 4718592  
141120.ov1 141120cb4 [0, 0, 0, -10542252, -13174915376] [2] 4718592  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 141120cb do not have complex multiplication.

Modular form 141120.2.a.cb

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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.