Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696eu |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
1517208151523328 = 218 · 33 · 118 |
Discriminant |
Eigenvalues |
2- 3+ 4 -2 11- -2 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-129228,17782160] |
[a1,a2,a3,a4,a6] |
Generators |
[770:19360:1] |
Generators of the group modulo torsion |
j |
19034163/121 |
j-invariant |
L |
8.196842416707 |
L(r)(E,1)/r! |
Ω |
0.47953668895629 |
Real period |
R |
2.1366567475934 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991343 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696r2 17424bi2 69696ew2 6336bn2 |
Quadratic twists by: -4 8 -3 -11 |