Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bq |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
4 |
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 |
[375256:7796517:343] |
Generators of the group modulo torsion |
j |
-9358714467168256/22284891 |
j-invariant |
L |
8.4487050258471 |
L(r)(E,1)/r! |
Ω |
0.30066849573254 |
Real period |
R |
7.0249337268006 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000965 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312co2 1083c2 3648f2 |
Quadratic twists by: -4 8 -19 |