Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cz |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3041280 |
Modular degree for the optimal curve |
Δ |
-3.8746418816906E+21 |
Discriminant |
Eigenvalues |
2+ 3- 3 2 11- -1 -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1489389,-2911977772] |
[a1,a2,a3,a4,a6] |
Generators |
[2033360867039032802105441145070512311266672:135834696321902562889926577080597313211306598:475798180191476126686031090912420549071] |
Generators of the group modulo torsion |
j |
36534162368/387420489 |
j-invariant |
L |
9.1889451508931 |
L(r)(E,1)/r! |
Ω |
0.068740647778664 |
Real period |
R |
66.837784104685 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696dc1 34848bd1 23232w1 69696db1 |
Quadratic twists by: -4 8 -3 -11 |