Atkin-Lehner |
2+ 3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
11970b |
Isogeny class |
Conductor |
11970 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
133120 |
Modular degree for the optimal curve |
Δ |
51661787627520000 = 226 · 33 · 54 · 74 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 2 0 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-402150,-97447500] |
[a1,a2,a3,a4,a6] |
Generators |
[-24300:52575:64] |
Generators of the group modulo torsion |
j |
266394205833287968827/1913399541760000 |
j-invariant |
L |
3.1118853463428 |
L(r)(E,1)/r! |
Ω |
0.18966644498635 |
Real period |
R |
4.101786885085 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95760cf1 11970bk1 59850ed1 83790p1 |
Quadratic twists by: -4 -3 5 -7 |