Atkin-Lehner |
2- 3- 5- 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
78390cd |
Isogeny class |
Conductor |
78390 |
Conductor |
∏ cp |
408 |
Product of Tamagawa factors cp |
deg |
783360 |
Modular degree for the optimal curve |
Δ |
-22855760658432000 = -1 · 217 · 36 · 53 · 134 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5- 1 3 13- -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-400862,98058349] |
[a1,a2,a3,a4,a6] |
Generators |
[397:-1369:1] |
Generators of the group modulo torsion |
j |
-9771918471960616089/31352209408000 |
j-invariant |
L |
12.20843510856 |
L(r)(E,1)/r! |
Ω |
0.38198907749861 |
Real period |
R |
0.078333745204202 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000814 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8710d1 |
Quadratic twists by: -3 |