Properties

Label 141120en
Number of curves $6$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.gx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.gx4 141120en1 [0, 0, 0, -309288, -66204488] [2] 786432 \(\Gamma_0(N)\)-optimal
141120.gx3 141120en2 [0, 0, 0, -318108, -62228432] [2, 2] 1572864  
141120.gx2 141120en3 [0, 0, 0, -1200108, 439100368] [2, 2] 3145728  
141120.gx5 141120en4 [0, 0, 0, 422772, -309089648] [2] 3145728  
141120.gx1 141120en5 [0, 0, 0, -18487308, 30594892048] [2] 6291456  
141120.gx6 141120en6 [0, 0, 0, 1975092, 2368351888] [2] 6291456  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.gx

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.