Atkin-Lehner |
3+ 5+ 7+ 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
128205b |
Isogeny class |
Conductor |
128205 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
72192 |
Modular degree for the optimal curve |
Δ |
-8609606775 = -1 · 33 · 52 · 7 · 113 · 372 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7+ 11- 2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,397,3162] |
[a1,a2,a3,a4,a6] |
Generators |
[8:-87:1] [214:1329:8] |
Generators of the group modulo torsion |
j |
256895581293/318874325 |
j-invariant |
L |
7.3923816150562 |
L(r)(E,1)/r! |
Ω |
0.87498921059683 |
Real period |
R |
1.40809005237 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999929948 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128205g1 |
Quadratic twists by: -3 |