Atkin-Lehner |
2+ 7- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
86632i |
Isogeny class |
Conductor |
86632 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12278784 |
Modular degree for the optimal curve |
Δ |
-4498544684154579968 = -1 · 210 · 77 · 13 · 177 |
Discriminant |
Eigenvalues |
2+ 1 0 7- 3 13- 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1013620288,-12421466399504] |
[a1,a2,a3,a4,a6] |
Generators |
[824517884792897788057536413831653289553071363317095963428085165624595798593827353854189705435567564:3196440033487024445746944875811764086757558389733108520374241356902049455104287501059206488653596351608:54861186647675333348084762904910722717434986817586299205470244178086186535015554034703553961] |
Generators of the group modulo torsion |
j |
-956007720229412472866500/37340819243 |
j-invariant |
L |
8.2606187179655 |
L(r)(E,1)/r! |
Ω |
0.013378293988054 |
Real period |
R |
154.36607099048 |
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 |
12376d1 |
Quadratic twists by: -7 |