Atkin-Lehner |
3+ 5+ 7- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
21945d |
Isogeny class |
Conductor |
21945 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5632 |
Modular degree for the optimal curve |
Δ |
-45623655 = -1 · 34 · 5 · 72 · 112 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- 11+ -6 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,64,-232] |
[a1,a2,a3,a4,a6] |
Generators |
[4:8:1] [12:43:1] |
Generators of the group modulo torsion |
j |
28962726911/45623655 |
j-invariant |
L |
4.1519467854445 |
L(r)(E,1)/r! |
Ω |
1.0662685184218 |
Real period |
R |
1.9469517826472 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
65835bn1 109725bi1 |
Quadratic twists by: -3 5 |