Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
67032x |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
2207644655182848 = 210 · 39 · 78 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- -6 2 -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-67179,6309142] |
[a1,a2,a3,a4,a6] |
Generators |
[791:21168:1] |
Generators of the group modulo torsion |
j |
381775972/25137 |
j-invariant |
L |
6.5252156594808 |
L(r)(E,1)/r! |
Ω |
0.45387468788689 |
Real period |
R |
1.7970862424973 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000194 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22344be1 9576j1 |
Quadratic twists by: -3 -7 |