Atkin-Lehner |
2- 3- 13- 19+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
42978v |
Isogeny class |
Conductor |
42978 |
Conductor |
∏ cp |
750 |
Product of Tamagawa factors cp |
deg |
1800000 |
Modular degree for the optimal curve |
Δ |
-1784804944651399008 = -1 · 25 · 315 · 135 · 192 · 29 |
Discriminant |
Eigenvalues |
2- 3- -4 -2 -3 13- -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-803575,284546441] |
[a1,a2,a3,a4,a6] |
Generators |
[-1030:4961:1] [-580:23861:1] |
Generators of the group modulo torsion |
j |
-57385609248046791394801/1784804944651399008 |
j-invariant |
L |
12.003721518238 |
L(r)(E,1)/r! |
Ω |
0.26347565705189 |
Real period |
R |
1.5186376422213 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
5 |
Number of elements in the torsion subgroup |
Twists |
128934r1 |
Quadratic twists by: -3 |