Atkin-Lehner |
2+ 3+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
60192a |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
2 |
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 |
[474:10314:1] |
Generators of the group modulo torsion |
j |
-157464/209 |
j-invariant |
L |
5.2259056297688 |
L(r)(E,1)/r! |
Ω |
0.57625385106658 |
Real period |
R |
4.5343780524223 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60192b1 120384cj1 60192l1 |
Quadratic twists by: -4 8 -3 |