Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
84474c |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
118368 |
Modular degree for the optimal curve |
Δ |
-66692814318 = -1 · 2 · 39 · 13 · 194 |
Discriminant |
Eigenvalues |
2+ 3+ -4 -2 4 13+ -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-609,13859] |
[a1,a2,a3,a4,a6] |
Generators |
[43:235:1] |
Generators of the group modulo torsion |
j |
-9747/26 |
j-invariant |
L |
2.3598286445557 |
L(r)(E,1)/r! |
Ω |
0.97132933730249 |
Real period |
R |
0.40491392455745 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002229 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84474bh1 84474bq1 |
Quadratic twists by: -3 -19 |