Atkin-Lehner |
2+ 3- 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360br |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
26 |
Product of Tamagawa factors cp |
deg |
718848 |
Modular degree for the optimal curve |
Δ |
-52336990732270320 = -1 · 24 · 313 · 5 · 177 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 5 -2 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-149220,-24816537] |
[a1,a2,a3,a4,a6] |
Generators |
[453:867:1] |
Generators of the group modulo torsion |
j |
-951468070144/135517455 |
j-invariant |
L |
8.3894530025403 |
L(r)(E,1)/r! |
Ω |
0.12050266048951 |
Real period |
R |
2.6777107493687 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000253 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34680bl1 4080c1 |
Quadratic twists by: -4 17 |