Atkin-Lehner |
3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
3003i |
Isogeny class |
Conductor |
3003 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
728 |
Modular degree for the optimal curve |
Δ |
-2189187 = -1 · 37 · 7 · 11 · 13 |
Discriminant |
Eigenvalues |
2 3- 0 7- 11+ 13- 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-98,-415] |
[a1,a2,a3,a4,a6] |
j |
-105154048000/2189187 |
j-invariant |
L |
5.2997688547448 |
L(r)(E,1)/r! |
Ω |
0.75710983639212 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48048bk1 9009n1 75075c1 21021c1 |
Quadratic twists by: -4 -3 5 -7 |