Atkin-Lehner |
3+ 7- 17- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
13209d |
Isogeny class |
Conductor |
13209 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
-1352504585851453251 = -1 · 312 · 77 · 174 · 37 |
Discriminant |
Eigenvalues |
0 3+ -3 7- 3 5 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-117237,58086650] |
[a1,a2,a3,a4,a6] |
Generators |
[1254:43375:1] |
Generators of the group modulo torsion |
j |
-178205665316766220288/1352504585851453251 |
j-invariant |
L |
2.6912526494245 |
L(r)(E,1)/r! |
Ω |
0.23242286531166 |
Real period |
R |
0.2067700308272 |
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 |
39627g1 92463g1 |
Quadratic twists by: -3 -7 |