Atkin-Lehner |
2+ 3+ 7- 13+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
33306b |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
2831360 |
Modular degree for the optimal curve |
Δ |
654718112574210048 = 228 · 3 · 75 · 13 · 612 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- -4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-50818274,139415806068] |
[a1,a2,a3,a4,a6] |
j |
14513877627086958322431944233/654718112574210048 |
j-invariant |
L |
1.0719178513627 |
L(r)(E,1)/r! |
Ω |
0.21438357027154 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99918ba1 |
Quadratic twists by: -3 |