Atkin-Lehner |
3+ 7- 19+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
17157d |
Isogeny class |
Conductor |
17157 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
72000 |
Modular degree for the optimal curve |
Δ |
-39463769612043 = -1 · 32 · 710 · 192 · 43 |
Discriminant |
Eigenvalues |
-2 3+ -2 7- -3 -1 5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,2736,-298096] |
[a1,a2,a3,a4,a6] |
Generators |
[456:-9776:1] [78:619:1] |
Generators of the group modulo torsion |
j |
2264191982563328/39463769612043 |
j-invariant |
L |
3.0635281632736 |
L(r)(E,1)/r! |
Ω |
0.31510756487341 |
Real period |
R |
0.24305415870489 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51471l1 120099r1 |
Quadratic twists by: -3 -7 |