Atkin-Lehner |
2+ 3- 29- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
31842n |
Isogeny class |
Conductor |
31842 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1741824 |
Modular degree for the optimal curve |
Δ |
-6189937363074613248 = -1 · 216 · 315 · 29 · 613 |
Discriminant |
Eigenvalues |
2+ 3- -4 -2 6 -7 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-140724,121449424] |
[a1,a2,a3,a4,a6] |
Generators |
[776:21500:1] |
Generators of the group modulo torsion |
j |
-422768317290285889/8490997754560512 |
j-invariant |
L |
2.5241102721472 |
L(r)(E,1)/r! |
Ω |
0.20064060033239 |
Real period |
R |
3.1450641943425 |
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 |
10614i1 |
Quadratic twists by: -3 |