Atkin-Lehner |
2- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
1232f |
Isogeny class |
Conductor |
1232 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
480 |
Modular degree for the optimal curve |
Δ |
-2207744 = -1 · 212 · 72 · 11 |
Discriminant |
Eigenvalues |
2- -1 3 7+ 11- -4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1429,-20323] |
[a1,a2,a3,a4,a6] |
Generators |
[44:7:1] |
Generators of the group modulo torsion |
j |
-78843215872/539 |
j-invariant |
L |
2.4916486789865 |
L(r)(E,1)/r! |
Ω |
0.38822723638015 |
Real period |
R |
3.2090080827645 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77b3 4928t1 11088bj1 30800bt1 |
Quadratic twists by: -4 8 -3 5 |