Atkin-Lehner |
2- 3+ 7- 17- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
87822w |
Isogeny class |
Conductor |
87822 |
Conductor |
∏ cp |
324 |
Product of Tamagawa factors cp |
deg |
342144 |
Modular degree for the optimal curve |
Δ |
-39159967504896 = -1 · 29 · 33 · 73 · 173 · 412 |
Discriminant |
Eigenvalues |
2- 3+ -3 7- -3 -1 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-23924,1461719] |
[a1,a2,a3,a4,a6] |
Generators |
[-177:445:1] [-143:1465:1] |
Generators of the group modulo torsion |
j |
-56084688300515139/1450369166848 |
j-invariant |
L |
13.940294536538 |
L(r)(E,1)/r! |
Ω |
0.64551490835362 |
Real period |
R |
0.59987832781099 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998057 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
87822a2 |
Quadratic twists by: -3 |