Atkin-Lehner |
2+ 3- 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970t |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-335194200 = -1 · 23 · 36 · 52 · 112 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 1 11- 1 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,96,-794] |
[a1,a2,a3,a4,a6] |
Generators |
[8:18:1] |
Generators of the group modulo torsion |
j |
820803071/2770200 |
j-invariant |
L |
5.295822222521 |
L(r)(E,1)/r! |
Ω |
0.87237215972194 |
Real period |
R |
0.50588331322243 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000459 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970co1 |
Quadratic twists by: -11 |