Atkin-Lehner |
2- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696bt |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
565248 |
Modular degree for the optimal curve |
Δ |
175505408 = 217 · 13 · 103 |
Discriminant |
Eigenvalues |
2- 0 2 -3 5 13+ 5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2178284,1237427792] |
[a1,a2,a3,a4,a6] |
Generators |
[23007:1:27] |
Generators of the group modulo torsion |
j |
8720819351266396194/1339 |
j-invariant |
L |
6.9542101433371 |
L(r)(E,1)/r! |
Ω |
0.72018214835846 |
Real period |
R |
2.4140455842261 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000432 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696d1 21424e1 |
Quadratic twists by: -4 8 |