Atkin-Lehner |
2+ 5+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69290a |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
645120 |
Modular degree for the optimal curve |
Δ |
337207518429184000 = 220 · 53 · 137 · 41 |
Discriminant |
Eigenvalues |
2+ 0 5+ 2 0 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-176890,6322356] |
[a1,a2,a3,a4,a6] |
Generators |
[77772:4090394:27] |
Generators of the group modulo torsion |
j |
126816226147521/69861376000 |
j-invariant |
L |
3.5681727432096 |
L(r)(E,1)/r! |
Ω |
0.26411012880873 |
Real period |
R |
6.755085006826 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001895 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5330g1 |
Quadratic twists by: 13 |