Atkin-Lehner |
2+ 3- 7- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
123354bb |
Isogeny class |
Conductor |
123354 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1186560 |
Modular degree for the optimal curve |
Δ |
-71970027822 = -1 · 2 · 37 · 75 · 11 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 11- -5 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1963962,-1058879318] |
[a1,a2,a3,a4,a6] |
Generators |
[17171:2233679:1] |
Generators of the group modulo torsion |
j |
-1149199821241342494625/98724318 |
j-invariant |
L |
4.0575966755906 |
L(r)(E,1)/r! |
Ω |
0.063765574745407 |
Real period |
R |
6.3633028846027 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000045427 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41118m1 |
Quadratic twists by: -3 |