Atkin-Lehner |
2- 13+ 101- |
Signs for the Atkin-Lehner involutions |
Class |
84032r |
Isogeny class |
Conductor |
84032 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
299520 |
Modular degree for the optimal curve |
Δ |
-4089511067779072 = -1 · 223 · 136 · 101 |
Discriminant |
Eigenvalues |
2- -2 0 1 0 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,39967,106399] |
[a1,a2,a3,a4,a6] |
Generators |
[3637:219700:1] |
Generators of the group modulo torsion |
j |
26932556234375/15600246688 |
j-invariant |
L |
3.8799540031631 |
L(r)(E,1)/r! |
Ω |
0.26329041059241 |
Real period |
R |
3.6841011336984 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000655 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84032f1 21008j1 |
Quadratic twists by: -4 8 |