Atkin-Lehner |
2- 5+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
13300j |
Isogeny class |
Conductor |
13300 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
40320 |
Modular degree for the optimal curve |
Δ |
-312946340000000 = -1 · 28 · 57 · 77 · 19 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- -2 0 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48508,4215512] |
[a1,a2,a3,a4,a6] |
Generators |
[-38:2450:1] |
Generators of the group modulo torsion |
j |
-3155824042576/78236585 |
j-invariant |
L |
3.6515276252819 |
L(r)(E,1)/r! |
Ω |
0.5431054584947 |
Real period |
R |
0.16008149536234 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53200bs1 119700z1 2660d1 93100s1 |
Quadratic twists by: -4 -3 5 -7 |