Atkin-Lehner |
2- 3+ 5+ 11- 103- |
Signs for the Atkin-Lehner involutions |
Class |
33990x |
Isogeny class |
Conductor |
33990 |
Conductor |
∏ cp |
140 |
Product of Tamagawa factors cp |
deg |
103040 |
Modular degree for the optimal curve |
Δ |
-477741686400 = -1 · 27 · 32 · 52 · 115 · 103 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -3 11- -5 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-23211,1351833] |
[a1,a2,a3,a4,a6] |
Generators |
[2217:-3542:27] [109:-418:1] |
Generators of the group modulo torsion |
j |
-1382949865068368689/477741686400 |
j-invariant |
L |
9.6469766259688 |
L(r)(E,1)/r! |
Ω |
0.91590679098705 |
Real period |
R |
0.075233611736335 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999979 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
101970y1 |
Quadratic twists by: -3 |