Atkin-Lehner |
2- 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400ea |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-110808000000000000 = -1 · 215 · 36 · 512 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ -1 0 1 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-108075,-21059750] |
[a1,a2,a3,a4,a6] |
Generators |
[9765:964400:1] |
Generators of the group modulo torsion |
j |
-2992209121/2375000 |
j-invariant |
L |
5.7975514421218 |
L(r)(E,1)/r! |
Ω |
0.12732191796069 |
Real period |
R |
5.69182385759 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000031 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8550bb1 7600k1 13680z1 |
Quadratic twists by: -4 -3 5 |