Atkin-Lehner |
2+ 5+ 23+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68080b |
Isogeny class |
Conductor |
68080 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
224640 |
Modular degree for the optimal curve |
Δ |
-6859631872000 = -1 · 211 · 53 · 232 · 373 |
Discriminant |
Eigenvalues |
2+ 0 5+ -1 3 4 -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-151043,22594658] |
[a1,a2,a3,a4,a6] |
Generators |
[226:46:1] |
Generators of the group modulo torsion |
j |
-186078231000531378/3349429625 |
j-invariant |
L |
5.5182952514118 |
L(r)(E,1)/r! |
Ω |
0.68733121322928 |
Real period |
R |
2.0071455891182 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996851 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34040b1 |
Quadratic twists by: -4 |