Atkin-Lehner |
2+ 3- 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400cp |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
259706250000 = 24 · 37 · 58 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5- 3 6 -2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6375,-194375] |
[a1,a2,a3,a4,a6] |
Generators |
[-350:225:8] |
Generators of the group modulo torsion |
j |
6288640/57 |
j-invariant |
L |
8.1616480757057 |
L(r)(E,1)/r! |
Ω |
0.53458535870559 |
Real period |
R |
1.2722707955734 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000293 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200dc1 22800bk1 68400bq1 |
Quadratic twists by: -4 -3 5 |