Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304dj |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-242424916651008 = -1 · 210 · 35 · 78 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 0 13+ 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,9931,-641733] |
[a1,a2,a3,a4,a6] |
Generators |
[142:1911:1] |
Generators of the group modulo torsion |
j |
899022848/2012283 |
j-invariant |
L |
7.2044763158816 |
L(r)(E,1)/r! |
Ω |
0.28825157127739 |
Real period |
R |
1.2496855190451 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000036831 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304fj1 7644c1 17472e1 |
Quadratic twists by: -4 8 -7 |