Atkin-Lehner |
3- 7- 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
13209g |
Isogeny class |
Conductor |
13209 |
Conductor |
∏ cp |
336 |
Product of Tamagawa factors cp |
deg |
236544 |
Modular degree for the optimal curve |
Δ |
-79096876330925691 = -1 · 38 · 77 · 172 · 373 |
Discriminant |
Eigenvalues |
-2 3- -3 7- -3 -5 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,104398,3846512] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:388:1] [2604:103933:27] |
Generators of the group modulo torsion |
j |
125833445519360233472/79096876330925691 |
j-invariant |
L |
3.6142057984636 |
L(r)(E,1)/r! |
Ω |
0.21286538501557 |
Real period |
R |
0.050532240719139 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39627k1 92463e1 |
Quadratic twists by: -3 -7 |