Atkin-Lehner |
3- 11- 19+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
33231i |
Isogeny class |
Conductor |
33231 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
529920 |
Modular degree for the optimal curve |
Δ |
-162068771729114613 = -1 · 316 · 113 · 19 · 533 |
Discriminant |
Eigenvalues |
1 3- -2 -3 11- 3 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-727217,239419181] |
[a1,a2,a3,a4,a6] |
Generators |
[4566:-28045:8] [531:-2015:1] |
Generators of the group modulo torsion |
j |
-42531913493187295080457/162068771729114613 |
j-invariant |
L |
10.256111450066 |
L(r)(E,1)/r! |
Ω |
0.32466779457325 |
Real period |
R |
0.21937191606771 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99693a1 |
Quadratic twists by: -3 |