Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192n |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
-2573414253589248 = -1 · 28 · 321 · 312 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 -4 -1 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,6324,-2433004] |
[a1,a2,a3,a4,a6] |
Generators |
[1156:39366:1] |
Generators of the group modulo torsion |
j |
155958272/14348907 |
j-invariant |
L |
4.2017149311337 |
L(r)(E,1)/r! |
Ω |
0.21680944382675 |
Real period |
R |
1.2112349837677 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000826 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064i1 69192e1 |
Quadratic twists by: -3 -31 |