Atkin-Lehner |
2- 11+ 17+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
68816i |
Isogeny class |
Conductor |
68816 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1309440 |
Modular degree for the optimal curve |
Δ |
-33147266004942848 = -1 · 223 · 112 · 175 · 23 |
Discriminant |
Eigenvalues |
2- -3 -2 5 11+ -6 17+ 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,46109,-7887134] |
[a1,a2,a3,a4,a6] |
Generators |
[175:2354:1] |
Generators of the group modulo torsion |
j |
2646798467571783/8092594239488 |
j-invariant |
L |
2.9891022636397 |
L(r)(E,1)/r! |
Ω |
0.18883375215275 |
Real period |
R |
3.9573199026637 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000296 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8602b1 |
Quadratic twists by: -4 |