Atkin-Lehner |
2- 3+ 5+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090bg |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
55737390240000 = 28 · 32 · 54 · 77 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 0 -6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-9556,12053] |
[a1,a2,a3,a4,a6] |
Generators |
[153:-1547:1] [-91:417:1] |
Generators of the group modulo torsion |
j |
820288712881/473760000 |
j-invariant |
L |
12.175717030543 |
L(r)(E,1)/r! |
Ω |
0.53359502278239 |
Real period |
R |
0.71307103881928 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9870t1 |
Quadratic twists by: -7 |