Properties

Label 141120lz
Number of curves 8
Conductor 141120
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.eg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120lz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.eg7 141120lz1 [0, 0, 0, -14042028, 20245391152] [2] 7077888 \(\Gamma_0(N)\)-optimal
141120.eg6 141120lz2 [0, 0, 0, -16299948, 13297319728] [2, 2] 14155776  
141120.eg5 141120lz3 [0, 0, 0, -41560428, -78374627408] [2] 21233664  
141120.eg8 141120lz4 [0, 0, 0, 54260052, 97658855728] [2] 28311552  
141120.eg4 141120lz5 [0, 0, 0, -122986668, -515740787408] [2] 28311552  
141120.eg2 141120lz6 [0, 0, 0, -619587948, -5935643093072] [2, 2] 42467328  
141120.eg3 141120lz7 [0, 0, 0, -574429548, -6837564721232] [2] 84934656  
141120.eg1 141120lz8 [0, 0, 0, -9913186668, -379898903267408] [2] 84934656  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.eg

sage: E.q_eigenform(10)
 
\( q - q^{5} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.