Atkin-Lehner |
2+ 3+ 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
16368h |
Isogeny class |
Conductor |
16368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-589740766447536 = -1 · 24 · 320 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 11- -2 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-16159,1416154] |
[a1,a2,a3,a4,a6] |
Generators |
[-521490:1509452:3375] |
Generators of the group modulo torsion |
j |
-29165810409306112/36858797902971 |
j-invariant |
L |
4.2834171648771 |
L(r)(E,1)/r! |
Ω |
0.46630678623522 |
Real period |
R |
9.1858349295316 |
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 |
8184g1 65472cm1 49104o1 |
Quadratic twists by: -4 8 -3 |