Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208bf |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-11150452359954432 = -1 · 232 · 32 · 73 · 292 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -4 4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-20568,5212656] |
[a1,a2,a3,a4,a6] |
Generators |
[-198:1218:1] |
Generators of the group modulo torsion |
j |
-684962743375/7936671744 |
j-invariant |
L |
5.2519859321257 |
L(r)(E,1)/r! |
Ω |
0.34340825239495 |
Real period |
R |
1.9117136435076 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001815 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8526h1 68208ck1 |
Quadratic twists by: -4 -7 |