Atkin-Lehner |
2- 3+ 11- 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
29172d |
Isogeny class |
Conductor |
29172 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
270720 |
Modular degree for the optimal curve |
Δ |
-9769062735514368 = -1 · 28 · 310 · 113 · 134 · 17 |
Discriminant |
Eigenvalues |
2- 3+ -2 -3 11- 13- 17- 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-256789,-50225327] |
[a1,a2,a3,a4,a6] |
Generators |
[1747:69498:1] |
Generators of the group modulo torsion |
j |
-7315005991668416512/38160401310603 |
j-invariant |
L |
3.2623033880187 |
L(r)(E,1)/r! |
Ω |
0.10600828900072 |
Real period |
R |
0.42741723034254 |
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 |
116688bc1 87516a1 |
Quadratic twists by: -4 -3 |