Atkin-Lehner |
2- 3+ 5+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090bh |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
250 |
Product of Tamagawa factors cp |
deg |
3192000 |
Modular degree for the optimal curve |
Δ |
2.828111479906E+19 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -6 3 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-899781,-206422581] |
[a1,a2,a3,a4,a6] |
Generators |
[-777:5324:1] [-531:11310:1] |
Generators of the group modulo torsion |
j |
1644137432066775806881/577165608144076800 |
j-invariant |
L |
12.135942543818 |
L(r)(E,1)/r! |
Ω |
0.15948426044904 |
Real period |
R |
0.30437969263262 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69090bu1 |
Quadratic twists by: -7 |