Properties

Label 141120.mc
Number of curves $8$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.mc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.mc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.mc1 141120jf7 [0, 0, 0, -182073612, 594925855216] [2] 42467328  
141120.mc2 141120jf4 [0, 0, 0, -162599052, 798040774384] [2] 14155776  
141120.mc3 141120jf6 [0, 0, 0, -76233612, -249380992784] [2, 2] 21233664  
141120.mc4 141120jf3 [0, 0, 0, -75669132, -253352899856] [2] 10616832  
141120.mc5 141120jf2 [0, 0, 0, -10189452, 12399768304] [2, 2] 7077888  
141120.mc6 141120jf5 [0, 0, 0, -2286732, 31141859056] [2] 14155776  
141120.mc7 141120jf1 [0, 0, 0, -1157772, -168717584] [2] 3538944 \(\Gamma_0(N)\)-optimal
141120.mc8 141120jf8 [0, 0, 0, 20574708, -839485788176] [2] 42467328  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.mc

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.