Atkin-Lehner |
2- 3+ 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936k |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
Δ |
-48118417228656 = -1 · 24 · 32 · 31 · 476 |
Discriminant |
Eigenvalues |
2- 3+ -3 1 0 -4 -6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-60122,5704011] |
[a1,a2,a3,a4,a6] |
Generators |
[137:141:1] |
Generators of the group modulo torsion |
j |
-1502142766461660928/3007401076791 |
j-invariant |
L |
3.4864476974559 |
L(r)(E,1)/r! |
Ω |
0.63670112459854 |
Real period |
R |
0.45631662459225 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002424 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17484e2 |
Quadratic twists by: -4 |