Atkin-Lehner |
2+ 11- 13- 43- |
Signs for the Atkin-Lehner involutions |
Class |
49192c |
Isogeny class |
Conductor |
49192 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
752640 |
Modular degree for the optimal curve |
Δ |
5851432296284432 = 24 · 115 · 134 · 433 |
Discriminant |
Eigenvalues |
2+ -2 -4 -5 11- 13- 0 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-138000,19339609] |
[a1,a2,a3,a4,a6] |
Generators |
[144:-1573:1] [-340:5203:1] |
Generators of the group modulo torsion |
j |
18165365296445952256/365714518517777 |
j-invariant |
L |
4.0261671712047 |
L(r)(E,1)/r! |
Ω |
0.42621074782055 |
Real period |
R |
0.078720194797868 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999981 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98384b1 |
Quadratic twists by: -4 |