Atkin-Lehner |
2+ 3- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
33984m |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-32107539456 = -1 · 210 · 312 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 -4 -6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,384,-8120] |
[a1,a2,a3,a4,a6] |
Generators |
[18:68:1] [62:504:1] |
Generators of the group modulo torsion |
j |
8388608/43011 |
j-invariant |
L |
7.4900788385645 |
L(r)(E,1)/r! |
Ω |
0.58798207248972 |
Real period |
R |
6.3693088522652 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33984bx1 2124b1 11328h1 |
Quadratic twists by: -4 8 -3 |