Atkin-Lehner |
2+ 3+ 5+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
690a |
Isogeny class |
Conductor |
690 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
448 |
Modular degree for the optimal curve |
Δ |
-2119680000 = -1 · 214 · 32 · 54 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 6 -2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,172,-1968] |
[a1,a2,a3,a4,a6] |
Generators |
[11:32:1] |
Generators of the group modulo torsion |
j |
557644990391/2119680000 |
j-invariant |
L |
1.3963979049939 |
L(r)(E,1)/r! |
Ω |
0.7448541863823 |
Real period |
R |
0.93736326553799 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5520bc1 22080bk1 2070s1 3450w1 |
Quadratic twists by: -4 8 -3 5 |