Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
8784o |
Isogeny class |
Conductor |
8784 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-37170944140640256 = -1 · 219 · 319 · 61 |
Discriminant |
Eigenvalues |
2- 3- 1 -2 2 4 -1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1021827,-397678718] |
[a1,a2,a3,a4,a6] |
Generators |
[1434890:33021513:1000] |
Generators of the group modulo torsion |
j |
-39515579724486529/12448473984 |
j-invariant |
L |
4.532472857159 |
L(r)(E,1)/r! |
Ω |
0.07507874566568 |
Real period |
R |
7.546198356426 |
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 |
1098c1 35136cl1 2928l1 |
Quadratic twists by: -4 8 -3 |