Atkin-Lehner |
2+ 3+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
60192b |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
19200 |
Modular degree for the optimal curve |
Δ |
-2106238464 = -1 · 29 · 39 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -1 0 11- 0 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243,2646] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:54:1] |
Generators of the group modulo torsion |
j |
-157464/209 |
j-invariant |
L |
5.2356646240849 |
L(r)(E,1)/r! |
Ω |
1.3240536602885 |
Real period |
R |
0.98856730304014 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999919 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60192a1 120384bz1 60192k1 |
Quadratic twists by: -4 8 -3 |