Atkin-Lehner |
3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033d |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
864000 |
Modular degree for the optimal curve |
Δ |
-3.2897949530831E+19 |
Discriminant |
Eigenvalues |
0 3+ 3 7+ 11- 13- -4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,798681,25723532] |
[a1,a2,a3,a4,a6] |
Generators |
[18330:2484553:1] |
Generators of the group modulo torsion |
j |
31804393380282368/18570034862379 |
j-invariant |
L |
4.0583188080822 |
L(r)(E,1)/r! |
Ω |
0.12550683500072 |
Real period |
R |
1.616772030009 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99099bd1 3003c1 |
Quadratic twists by: -3 -11 |