Atkin-Lehner |
2+ 3- 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
19536p |
Isogeny class |
Conductor |
19536 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
Δ |
-589599998355456 = -1 · 211 · 312 · 114 · 37 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 11- -2 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-27824,2125236] |
[a1,a2,a3,a4,a6] |
Generators |
[-170:1404:1] [-164:1518:1] |
Generators of the group modulo torsion |
j |
-1163236610689634/287890624197 |
j-invariant |
L |
7.2043429789128 |
L(r)(E,1)/r! |
Ω |
0.49158216868838 |
Real period |
R |
1.221284971567 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
9768n4 78144br3 58608g3 |
Quadratic twists by: -4 8 -3 |