Atkin-Lehner |
2+ 7- 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
77168c |
Isogeny class |
Conductor |
77168 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
657408 |
Modular degree for the optimal curve |
Δ |
-6712432439195392 = -1 · 28 · 7 · 132 · 536 |
Discriminant |
Eigenvalues |
2+ -2 0 7- 4 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-198108,-34233428] |
[a1,a2,a3,a4,a6] |
Generators |
[12439:1386480:1] |
Generators of the group modulo torsion |
j |
-3358860597729250000/26220439215607 |
j-invariant |
L |
4.1667492428757 |
L(r)(E,1)/r! |
Ω |
0.11309449233174 |
Real period |
R |
6.1405130550978 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007534 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38584a1 |
Quadratic twists by: -4 |