Atkin-Lehner |
2+ 3+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312b |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
Δ |
-1076306734743552 = -1 · 219 · 32 · 133 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 -6 13+ 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,25087,-398847] |
[a1,a2,a3,a4,a6] |
Generators |
[227:4116:1] |
Generators of the group modulo torsion |
j |
6660589493375/4105784358 |
j-invariant |
L |
5.150691996947 |
L(r)(E,1)/r! |
Ω |
0.28365042696984 |
Real period |
R |
4.5396476428028 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000054852 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cu2 3666n2 |
Quadratic twists by: -4 8 |