Properties

Label 51984cq
Number of curves 22
Conductor 5198451984
CM no
Rank 00
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("cq1") E.isogeny_class()
 

Elliptic curves in class 51984cq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51984.z2 51984cq1 [0,0,0,1022352,454449904][0, 0, 0, 1022352, 454449904] 841232384/1121931841232384/1121931 157606901180488986624-157606901180488986624 [][] 13824001382400 2.56142.5614 Γ0(N)\Gamma_0(N)-optimal
51984.z1 51984cq2 [0,0,0,228227088,1327088209264][0, 0, 0, -228227088, 1327088209264] 9358714467168256/22284891-9358714467168256/22284891 3130542443033456062464-3130542443033456062464 [][] 69120006912000 3.36613.3661  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 51984cq have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
191911
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
55 13T+5T2 1 - 3 T + 5 T^{2} 1.5.ad
77 15T+7T2 1 - 5 T + 7 T^{2} 1.7.af
1111 1T+11T2 1 - T + 11 T^{2} 1.11.ab
1313 1+2T+13T2 1 + 2 T + 13 T^{2} 1.13.c
1717 1T+17T2 1 - T + 17 T^{2} 1.17.ab
2323 1+4T+23T2 1 + 4 T + 23 T^{2} 1.23.e
2929 1+2T+29T2 1 + 2 T + 29 T^{2} 1.29.c
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 51984cq do not have complex multiplication.

Modular form 51984.2.a.cq

Copy content sage:E.q_eigenform(10)
 
qq53q73q11+6q133q17+O(q20)q - q^{5} - 3 q^{7} - 3 q^{11} + 6 q^{13} - 3 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.

(1551)\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.