Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
38304q |
Isogeny class |
Conductor |
38304 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
5534442503618112 = 26 · 37 · 78 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 4 4 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-47325,-1700372] |
[a1,a2,a3,a4,a6] |
Generators |
[-184:882:1] |
Generators of the group modulo torsion |
j |
251239591000000/118622310177 |
j-invariant |
L |
6.8388343091982 |
L(r)(E,1)/r! |
Ω |
0.33896883120309 |
Real period |
R |
1.2609629705713 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38304bk1 76608cm1 12768bb1 |
Quadratic twists by: -4 8 -3 |