Atkin-Lehner |
2+ 3- 5- 7+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
37170k |
Isogeny class |
Conductor |
37170 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
233472 |
Modular degree for the optimal curve |
Δ |
-812907900000000 = -1 · 28 · 39 · 58 · 7 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ -4 -6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-27909,2265813] |
[a1,a2,a3,a4,a6] |
Generators |
[177:-1776:1] |
Generators of the group modulo torsion |
j |
-3297902135604049/1115100000000 |
j-invariant |
L |
3.1629160499108 |
L(r)(E,1)/r! |
Ω |
0.47407612981461 |
Real period |
R |
0.41698419449359 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12390s1 |
Quadratic twists by: -3 |