Atkin-Lehner |
2- 3+ 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936s |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
16896 |
Modular degree for the optimal curve |
Δ |
-9860976 = -1 · 24 · 32 · 31 · 472 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 2 0 -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-222,1359] |
[a1,a2,a3,a4,a6] |
Generators |
[42:141:8] [9:3:1] |
Generators of the group modulo torsion |
j |
-75965686528/616311 |
j-invariant |
L |
6.8141274838872 |
L(r)(E,1)/r! |
Ω |
2.3066614833245 |
Real period |
R |
0.73852703714461 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999801 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17484d1 |
Quadratic twists by: -4 |