Atkin-Lehner |
2+ 3+ 41+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
31734a |
Isogeny class |
Conductor |
31734 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12032 |
Modular degree for the optimal curve |
Δ |
-31226256 = -1 · 24 · 33 · 412 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -3 1 -5 1 -8 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-66,356] |
[a1,a2,a3,a4,a6] |
Generators |
[40:226:1] [4:-14:1] |
Generators of the group modulo torsion |
j |
-1187648379/1156528 |
j-invariant |
L |
5.4115847576596 |
L(r)(E,1)/r! |
Ω |
1.899993346613 |
Real period |
R |
0.35602655973153 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
31734j1 |
Quadratic twists by: -3 |