Atkin-Lehner |
2- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
120032f |
Isogeny class |
Conductor |
120032 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
145920 |
Modular degree for the optimal curve |
Δ |
-309300378112 = -1 · 29 · 117 · 31 |
Discriminant |
Eigenvalues |
2- 0 2 1 11- 4 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21659,1227182] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:1210:1] |
Generators of the group modulo torsion |
j |
-1238833224/341 |
j-invariant |
L |
8.9085180576649 |
L(r)(E,1)/r! |
Ω |
0.94611829505876 |
Real period |
R |
1.1769825723723 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000112444 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120032d1 10912b1 |
Quadratic twists by: -4 -11 |