Atkin-Lehner |
2- 3+ 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970bl |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
132 |
Product of Tamagawa factors cp |
deg |
1672704 |
Modular degree for the optimal curve |
Δ |
-6097576588651468800 = -1 · 211 · 34 · 52 · 118 · 193 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 1 11- 5 -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,417629,-57476671] |
[a1,a2,a3,a4,a6] |
Generators |
[1139:42990:1] |
Generators of the group modulo torsion |
j |
37579769391791/28445644800 |
j-invariant |
L |
8.177748533283 |
L(r)(E,1)/r! |
Ω |
0.13347084802456 |
Real period |
R |
0.46416608064886 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992284 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970f1 |
Quadratic twists by: -11 |