Atkin-Lehner |
2+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
45472i |
Isogeny class |
Conductor |
45472 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
136192 |
Modular degree for the optimal curve |
Δ |
-4793362853888 = -1 · 212 · 79 · 29 |
Discriminant |
Eigenvalues |
2+ -1 0 7- -2 2 6 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-141773,-20499611] |
[a1,a2,a3,a4,a6] |
j |
-1906624000/29 |
j-invariant |
L |
1.9682964431273 |
L(r)(E,1)/r! |
Ω |
0.1230185277068 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45472d1 90944dn1 45472e1 |
Quadratic twists by: -4 8 -7 |