Atkin-Lehner |
3- 5+ 7+ 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
128205o |
Isogeny class |
Conductor |
128205 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
227840 |
Modular degree for the optimal curve |
Δ |
-12617295075 = -1 · 311 · 52 · 7 · 11 · 37 |
Discriminant |
Eigenvalues |
2 3- 5+ 7+ 11- -4 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-9183,-338751] |
[a1,a2,a3,a4,a6] |
Generators |
[61768:284459:512] |
Generators of the group modulo torsion |
j |
-117476212658176/17307675 |
j-invariant |
L |
11.807308506169 |
L(r)(E,1)/r! |
Ω |
0.24384821128831 |
Real period |
R |
6.0525913228935 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999969676 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42735l1 |
Quadratic twists by: -3 |