Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("141120.ej1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ej2 141120hi1 [0, 0, 0, -329868, 72831248] [2] 884736 \(\Gamma_0(N)\)-optimal
141120.ej3 141120hi2 [0, 0, 0, -235788, 115242512] [2] 1769472  
141120.ej1 141120hi3 [0, 0, 0, -1317708, -510169968] [2] 2654208  
141120.ej4 141120hi4 [0, 0, 0, 2069172, -2700803952] [2] 5308416  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.ej

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.