Properties

Label 141120jy
Number of curves 44
Conductor 141120141120
CM no
Rank 00
Graph

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Copy content sage:E = EllipticCurve("jy1") E.isogeny_class()
 

Elliptic curves in class 141120jy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.oq4 141120jy1 [0,0,0,65268,10224144][0, 0, 0, 65268, -10224144] 1367631/28001367631/2800 62952607265587200-62952607265587200 [2][2] 11796481179648 1.90781.9078 Γ0(N)\Gamma_0(N)-optimal
141120.oq3 141120jy2 [0,0,0,499212,109798416][0, 0, 0, -499212, -109798416] 611960049/122500611960049/122500 27541765678694400002754176567869440000 [2,2][2, 2] 23592962359296 2.25442.2544  
141120.oq2 141120jy3 [0,0,0,2474892,1400411376][0, 0, 0, -2474892, 1400411376] 74565301329/546875074565301329/5468750 122954311065600000000122954311065600000000 [2][2] 47185924718592 2.60102.6010  
141120.oq1 141120jy4 [0,0,0,7555212,7992761616][0, 0, 0, -7555212, -7992761616] 2121328796049/1200502121328796049/120050 26990930365120512002699093036512051200 [2][2] 47185924718592 2.60102.6010  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 141120jy have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
551T1 - T
7711
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
1111 1+2T+11T2 1 + 2 T + 11 T^{2} 1.11.c
1313 1+6T+13T2 1 + 6 T + 13 T^{2} 1.13.g
1717 1+2T+17T2 1 + 2 T + 17 T^{2} 1.17.c
1919 1+4T+19T2 1 + 4 T + 19 T^{2} 1.19.e
2323 1+2T+23T2 1 + 2 T + 23 T^{2} 1.23.c
2929 1+29T2 1 + 29 T^{2} 1.29.a
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 141120jy do not have complex multiplication.

Modular form 141120.2.a.jy

Copy content sage:E.q_eigenform(10)
 
q+q5+4q116q13+2q17+O(q20)q + q^{5} + 4 q^{11} - 6 q^{13} + 2 q^{17} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.