Atkin-Lehner |
2- 3+ 5+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970br |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
52 |
Product of Tamagawa factors cp |
deg |
79872 |
Modular degree for the optimal curve |
Δ |
-4237516800 = -1 · 213 · 32 · 52 · 112 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -3 11- -1 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-2736,54033] |
[a1,a2,a3,a4,a6] |
Generators |
[21:-91:1] [-11:293:1] |
Generators of the group modulo torsion |
j |
-18719599019209/35020800 |
j-invariant |
L |
11.653005832736 |
L(r)(E,1)/r! |
Ω |
1.38564947006 |
Real period |
R |
0.16172651948187 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999759 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970d1 |
Quadratic twists by: -11 |