Atkin-Lehner |
3- 5+ 31+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
82305c |
Isogeny class |
Conductor |
82305 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1853440 |
Modular degree for the optimal curve |
Δ |
179362368827690625 = 322 · 55 · 31 · 59 |
Discriminant |
Eigenvalues |
-1 3- 5+ -4 4 6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1091363,-438089358] |
[a1,a2,a3,a4,a6] |
Generators |
[4123240346126:75573868388349:2992209121] |
Generators of the group modulo torsion |
j |
197198446243986541801/246038914715625 |
j-invariant |
L |
2.4587068881468 |
L(r)(E,1)/r! |
Ω |
0.14772017599092 |
Real period |
R |
16.644353892259 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007838 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27435a1 |
Quadratic twists by: -3 |