Atkin-Lehner |
2+ 3- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
12342k |
Isogeny class |
Conductor |
12342 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
8803853167239364608 = 228 · 32 · 118 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 11- 2 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-707490,179061364] |
[a1,a2,a3,a4,a6] |
Generators |
[12559885:3320976537:274625] |
Generators of the group modulo torsion |
j |
22106889268753393/4969545596928 |
j-invariant |
L |
4.2305476383997 |
L(r)(E,1)/r! |
Ω |
0.21834918082463 |
Real period |
R |
9.6875738723234 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
98736by1 37026bm1 1122k1 |
Quadratic twists by: -4 -3 -11 |