Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("141120.ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120pp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ek2 141120pp1 [0, 0, 0, -329868, -72831248] [2] 884736 \(\Gamma_0(N)\)-optimal
141120.ek3 141120pp2 [0, 0, 0, -235788, -115242512] [2] 1769472  
141120.ek1 141120pp3 [0, 0, 0, -1317708, 510169968] [2] 2654208  
141120.ek4 141120pp4 [0, 0, 0, 2069172, 2700803952] [2] 5308416  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.ek

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.