Atkin-Lehner |
3+ 17- 53- |
Signs for the Atkin-Lehner involutions |
Class |
8109b |
Isogeny class |
Conductor |
8109 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
8352 |
Modular degree for the optimal curve |
Δ |
49815881847 = 39 · 17 · 533 |
Discriminant |
Eigenvalues |
-1 3+ -2 -5 -6 1 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2351,43120] |
[a1,a2,a3,a4,a6] |
Generators |
[88:-760:1] |
Generators of the group modulo torsion |
j |
72982227339/2530909 |
j-invariant |
L |
1.2833650101063 |
L(r)(E,1)/r! |
Ω |
1.1201402598272 |
Real period |
R |
0.19095302260098 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129744u1 8109a1 |
Quadratic twists by: -4 -3 |