Atkin-Lehner |
3+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
33969a |
Isogeny class |
Conductor |
33969 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-113512067253 = -1 · 33 · 137 · 67 |
Discriminant |
Eigenvalues |
1 3+ -2 -2 3 13+ -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-4566,-121779] |
[a1,a2,a3,a4,a6] |
Generators |
[950:7637:8] |
Generators of the group modulo torsion |
j |
-2181825073/23517 |
j-invariant |
L |
3.7659864235959 |
L(r)(E,1)/r! |
Ω |
0.29019787644141 |
Real period |
R |
3.2443263108752 |
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 |
101907e1 2613a1 |
Quadratic twists by: -3 13 |