Atkin-Lehner |
2+ 3- 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
117216m |
Isogeny class |
Conductor |
117216 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-2224142654976 = -1 · 29 · 36 · 115 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 1 -2 11- 6 -1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8067,-287962] |
[a1,a2,a3,a4,a6] |
Generators |
[169:1782:1] |
Generators of the group modulo torsion |
j |
-155547270152/5958887 |
j-invariant |
L |
8.4893734542365 |
L(r)(E,1)/r! |
Ω |
0.25131398594624 |
Real period |
R |
1.6889974219762 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999609407 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117216e1 13024c1 |
Quadratic twists by: -4 -3 |