Atkin-Lehner |
2+ 7- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
33418n |
Isogeny class |
Conductor |
33418 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
550368 |
Modular degree for the optimal curve |
Δ |
-130334929574148992 = -1 · 27 · 710 · 112 · 313 |
Discriminant |
Eigenvalues |
2+ 1 4 7- 11- -5 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-92489,-20474996] |
[a1,a2,a3,a4,a6] |
Generators |
[173351193255710:-16033482192041539:20458415375] |
Generators of the group modulo torsion |
j |
-309746789401/461403008 |
j-invariant |
L |
6.159883732001 |
L(r)(E,1)/r! |
Ω |
0.12997335003197 |
Real period |
R |
23.696718329126 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33418f1 |
Quadratic twists by: -7 |