Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("141120.md1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.md7 141120bd1 [0, 0, 0, -1157772, 168717584] [2] 3538944 \(\Gamma_0(N)\)-optimal
141120.md5 141120bd2 [0, 0, 0, -10189452, -12399768304] [2, 2] 7077888  
141120.md4 141120bd3 [0, 0, 0, -75669132, 253352899856] [2] 10616832  
141120.md6 141120bd4 [0, 0, 0, -2286732, -31141859056] [2] 14155776  
141120.md2 141120bd5 [0, 0, 0, -162599052, -798040774384] [2] 14155776  
141120.md3 141120bd6 [0, 0, 0, -76233612, 249380992784] [2, 2] 21233664  
141120.md8 141120bd7 [0, 0, 0, 20574708, 839485788176] [2] 42467328  
141120.md1 141120bd8 [0, 0, 0, -182073612, -594925855216] [2] 42467328  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.md

sage: E.q_eigenform(10)
 
\( q + q^{5} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.