Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696bs |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-37928255422464 = -1 · 216 · 314 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -1 0 11- -1 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,8052,102256] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:144:1] |
Generators of the group modulo torsion |
j |
9987164/6561 |
j-invariant |
L |
5.5315468045568 |
L(r)(E,1)/r! |
Ω |
0.40615223614807 |
Real period |
R |
1.7024240887486 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000752 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696ga1 8712i1 23232bp1 69696br1 |
Quadratic twists by: -4 8 -3 -11 |