Properties

Label 141120el
Number of curves 8
Conductor 141120
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.gt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.gt7 141120el1 [0, 0, 0, 5926452, -4184495728] [2] 9437184 \(\Gamma_0(N)\)-optimal
141120.gt6 141120el2 [0, 0, 0, -30200268, -37464430192] [2, 2] 18874368  
141120.gt5 141120el3 [0, 0, 0, -213091788, 1170570637712] [2, 2] 37748736  
141120.gt4 141120el4 [0, 0, 0, -425336268, -3375415303792] [2] 37748736  
141120.gt2 141120el5 [0, 0, 0, -3388291788, 75913508557712] [2, 2] 75497472  
141120.gt8 141120el6 [0, 0, 0, 35843892, 3741877063568] [2] 75497472  
141120.gt1 141120el7 [0, 0, 0, -54212659788, 4858466207610512] [2] 150994944  
141120.gt3 141120el8 [0, 0, 0, -3367123788, 76908836384912] [2] 150994944  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.gt

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.