Atkin-Lehner |
2- 3+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
23856s |
Isogeny class |
Conductor |
23856 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-160275677184 = -1 · 214 · 39 · 7 · 71 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- -1 3 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3416,-78096] |
[a1,a2,a3,a4,a6] |
Generators |
[172:2096:1] |
Generators of the group modulo torsion |
j |
-1076575468249/39129804 |
j-invariant |
L |
4.4780265410147 |
L(r)(E,1)/r! |
Ω |
0.31156843972444 |
Real period |
R |
3.5931323347249 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2982c1 95424ck1 71568bx1 |
Quadratic twists by: -4 8 -3 |