Atkin-Lehner |
2+ 3+ 17+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
67728b |
Isogeny class |
Conductor |
67728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1509120 |
Modular degree for the optimal curve |
Δ |
-17035177375601712 = -1 · 24 · 312 · 176 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 4 4 0 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1193831,-501709362] |
[a1,a2,a3,a4,a6] |
Generators |
[78922705717172774531912311654000187288003534689482512373339784831108127052316130:2842525913348115795710476565659618803194262900564055357208058463438695352244972124:39178123659816054709373067499452486769945828932433525164474272722962697831375] |
Generators of the group modulo torsion |
j |
-11760685844531533256704/1064698585975107 |
j-invariant |
L |
8.8218117934807 |
L(r)(E,1)/r! |
Ω |
0.072215671987599 |
Real period |
R |
122.15924259482 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33864k1 |
Quadratic twists by: -4 |