Atkin-Lehner |
2+ 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
117216b |
Isogeny class |
Conductor |
117216 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
270336 |
Modular degree for the optimal curve |
Δ |
4310510326848 = 26 · 33 · 113 · 374 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -2 11+ 2 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6693,-185580] |
[a1,a2,a3,a4,a6] |
Generators |
[-58310:80197:1000] |
Generators of the group modulo torsion |
j |
19188562851648/2494508291 |
j-invariant |
L |
9.32655891297 |
L(r)(E,1)/r! |
Ω |
0.53235473703785 |
Real period |
R |
8.759721934768 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999772197 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117216x1 117216y1 |
Quadratic twists by: -4 -3 |