Atkin-Lehner |
3- 19+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8037c |
Isogeny class |
Conductor |
8037 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8320 |
Modular degree for the optimal curve |
Δ |
3005653149 = 311 · 192 · 47 |
Discriminant |
Eigenvalues |
2 3- 1 1 -1 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-11307,-462767] |
[a1,a2,a3,a4,a6] |
Generators |
[-3932:139:64] |
Generators of the group modulo torsion |
j |
219299862974464/4122981 |
j-invariant |
L |
8.728960265307 |
L(r)(E,1)/r! |
Ω |
0.46298102975403 |
Real period |
R |
2.3567273020734 |
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 |
128592i1 2679a1 |
Quadratic twists by: -4 -3 |