Atkin-Lehner |
3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
33033i |
Isogeny class |
Conductor |
33033 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
7384608 |
Modular degree for the optimal curve |
Δ |
-2.2424338998532E+23 |
Discriminant |
Eigenvalues |
-1 3+ 4 7+ 11- 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-63849706,-197718966664] |
[a1,a2,a3,a4,a6] |
Generators |
[6598325630:-47943032082691:125] |
Generators of the group modulo torsion |
j |
-1109873716015912969/8645553420777 |
j-invariant |
L |
3.9238311045903 |
L(r)(E,1)/r! |
Ω |
0.026691799032392 |
Real period |
R |
21.000731347314 |
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 |
99099bi1 33033n1 |
Quadratic twists by: -3 -11 |