Atkin-Lehner |
2+ 3+ 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970b |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
49008960 |
Modular degree for the optimal curve |
Δ |
-2.0113920497681E+27 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 11- -2 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1049591633,13264402599573] |
[a1,a2,a3,a4,a6] |
j |
-4930125119275609518529/77547870720000000 |
j-invariant |
L |
0.046694720606154 |
L(r)(E,1)/r! |
Ω |
0.046694725498125 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970bp1 |
Quadratic twists by: -11 |