Atkin-Lehner |
3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619a |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
5 |
Product of Tamagawa factors cp |
deg |
10800 |
Modular degree for the optimal curve |
Δ |
-1094918465979 = -1 · 33 · 134 · 175 |
Discriminant |
Eigenvalues |
1 3+ -1 2 3 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,842,-49109] |
[a1,a2,a3,a4,a6] |
j |
2307174311/38336139 |
j-invariant |
L |
2.1261134687377 |
L(r)(E,1)/r! |
Ω |
0.42522269374755 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25857g1 8619c1 |
Quadratic twists by: -3 13 |