Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208bl |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
272160 |
Modular degree for the optimal curve |
Δ |
-783294435674352 = -1 · 24 · 315 · 76 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- -3 -5 1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4622,1353507] |
[a1,a2,a3,a4,a6] |
Generators |
[-20878153:179339623:205379] |
Generators of the group modulo torsion |
j |
-5802287872/416118303 |
j-invariant |
L |
5.5900521941338 |
L(r)(E,1)/r! |
Ω |
0.41580717194603 |
Real period |
R |
13.443857085372 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999989605 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17052m1 1392n1 |
Quadratic twists by: -4 -7 |