Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312co |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-67098389125374144 = -1 · 26 · 32 · 1911 |
Discriminant |
Eigenvalues |
2- 3+ -1 -3 -3 -6 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6339641,-6141813681] |
[a1,a2,a3,a4,a6] |
Generators |
[3911182:32449929:1331] |
Generators of the group modulo torsion |
j |
-9358714467168256/22284891 |
j-invariant |
L |
2.2868953457121 |
L(r)(E,1)/r! |
Ω |
0.047572209732676 |
Real period |
R |
6.0090107172809 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312bq2 17328bf2 3648be2 |
Quadratic twists by: -4 8 -19 |