Atkin-Lehner |
2- 3+ 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360cn |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
725760 |
Modular degree for the optimal curve |
Δ |
-1618030080000000000 = -1 · 218 · 37 · 510 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 5- -1 2 1 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-67960,61601392] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:8000:1] |
Generators of the group modulo torsion |
j |
-29324621982169/1366875000000 |
j-invariant |
L |
5.6842382633177 |
L(r)(E,1)/r! |
Ω |
0.22136396596444 |
Real period |
R |
0.64195613759207 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993208 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8670j1 69360dg1 |
Quadratic twists by: -4 17 |