Atkin-Lehner |
2- 3+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
9768n |
Isogeny class |
Conductor |
9768 |
Conductor |
∏ cp |
4 |
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 |
[1366448252371523:-27514304170013430:2879651915083] |
Generators of the group modulo torsion |
j |
-1163236610689634/287890624197 |
j-invariant |
L |
3.6096771518593 |
L(r)(E,1)/r! |
Ω |
0.18244743220455 |
Real period |
R |
19.784751740504 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19536p4 78144bk3 29304f3 107448e3 |
Quadratic twists by: -4 8 -3 -11 |