Atkin-Lehner |
2+ 19- 23- |
Signs for the Atkin-Lehner involutions |
Class |
27968v |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
1387645246904467456 = 243 · 193 · 23 |
Discriminant |
Eigenvalues |
2+ 3 -1 2 -5 2 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-844108,293070704] |
[a1,a2,a3,a4,a6] |
Generators |
[767646:17432576:729] |
Generators of the group modulo torsion |
j |
253733516886870441/5293446529024 |
j-invariant |
L |
9.4933828065444 |
L(r)(E,1)/r! |
Ω |
0.27012053212381 |
Real period |
R |
2.9287489834948 |
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 |
27968bk1 874b1 |
Quadratic twists by: -4 8 |