Atkin-Lehner |
2+ 3- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176u |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
-6639785027156736 = -1 · 28 · 310 · 7 · 137 |
Discriminant |
Eigenvalues |
2+ 3- -3 7+ -2 13+ 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,34476,-3049436] |
[a1,a2,a3,a4,a6] |
Generators |
[78:338:1] [182:-3042:1] |
Generators of the group modulo torsion |
j |
5030912/7371 |
j-invariant |
L |
8.8205039945698 |
L(r)(E,1)/r! |
Ω |
0.2235675201338 |
Real period |
R |
1.2329194762812 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997621 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28392ba1 6552w1 |
Quadratic twists by: -3 13 |