Atkin-Lehner |
2+ 3- 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
111720r |
Isogeny class |
Conductor |
111720 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-212840006400 = -1 · 28 · 36 · 52 · 74 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -3 0 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3201,72099] |
[a1,a2,a3,a4,a6] |
Generators |
[-66:15:1] [-33:-378:1] |
Generators of the group modulo torsion |
j |
-5903156224/346275 |
j-invariant |
L |
13.233341105381 |
L(r)(E,1)/r! |
Ω |
0.9851703682365 |
Real period |
R |
0.093281532898539 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000586 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111720q1 |
Quadratic twists by: -7 |