Atkin-Lehner |
3+ 17+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
122247c |
Isogeny class |
Conductor |
122247 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
22329689219469 = 39 · 176 · 47 |
Discriminant |
Eigenvalues |
2 3+ -3 -1 3 0 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-23409,-1359673] |
[a1,a2,a3,a4,a6] |
Generators |
[-750:833:8] [3570:70223:8] |
Generators of the group modulo torsion |
j |
2985984/47 |
j-invariant |
L |
19.437824494694 |
L(r)(E,1)/r! |
Ω |
0.38633863515168 |
Real period |
R |
12.578229773011 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000112 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122247b1 423d1 |
Quadratic twists by: -3 17 |