Atkin-Lehner |
2+ 3+ 5- 7- 83- |
Signs for the Atkin-Lehner involutions |
Class |
17430j |
Isogeny class |
Conductor |
17430 |
Conductor |
∏ cp |
140 |
Product of Tamagawa factors cp |
deg |
51520 |
Modular degree for the optimal curve |
Δ |
-3923384062500 = -1 · 22 · 32 · 57 · 75 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- -6 -4 -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-3572,124356] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:89:1] [-38:474:1] |
Generators of the group modulo torsion |
j |
-5042524562477641/3923384062500 |
j-invariant |
L |
4.8729031559761 |
L(r)(E,1)/r! |
Ω |
0.71956299285569 |
Real period |
R |
0.04837165259983 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52290cd1 87150co1 122010t1 |
Quadratic twists by: -3 5 -7 |