Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cu |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-208694022647808 = -1 · 212 · 3 · 198 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 -6 -2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3369,700233] |
[a1,a2,a3,a4,a6] |
Generators |
[203:2888:1] |
Generators of the group modulo torsion |
j |
-21952/1083 |
j-invariant |
L |
1.7989165683001 |
L(r)(E,1)/r! |
Ω |
0.46653620030643 |
Real period |
R |
1.9279496067322 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002701 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312dr2 34656s1 3648bi2 |
Quadratic twists by: -4 8 -19 |