Atkin-Lehner |
2+ 3- 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
28272c |
Isogeny class |
Conductor |
28272 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-25784064 = -1 · 28 · 32 · 192 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 6 4 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,68,140] |
[a1,a2,a3,a4,a6] |
Generators |
[23:120:1] |
Generators of the group modulo torsion |
j |
133846832/100719 |
j-invariant |
L |
7.5609505556596 |
L(r)(E,1)/r! |
Ω |
1.3543510620456 |
Real period |
R |
2.7913554939882 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14136a1 113088bb1 84816d1 |
Quadratic twists by: -4 8 -3 |