Atkin-Lehner |
5+ 7- 13- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
84175f |
Isogeny class |
Conductor |
84175 |
Conductor |
∏ cp |
132 |
Product of Tamagawa factors cp |
deg |
8731008 |
Modular degree for the optimal curve |
Δ |
7.2162001813286E+21 |
Discriminant |
Eigenvalues |
-2 1 5+ 7- -6 13- -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-14870198,-21694301246] |
[a1,a2,a3,a4,a6] |
Generators |
[-2443:7689:1] |
Generators of the group modulo torsion |
j |
14545678577070551268536320/288648007253142788797 |
j-invariant |
L |
2.9076019666735 |
L(r)(E,1)/r! |
Ω |
0.076974004354789 |
Real period |
R |
0.28616528176117 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999917559 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84175j1 |
Quadratic twists by: 5 |