Atkin-Lehner |
2- 13- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
69056o |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
958464 |
Modular degree for the optimal curve |
Δ |
-68496375444144128 = -1 · 222 · 134 · 833 |
Discriminant |
Eigenvalues |
2- 3 -2 -1 -5 13- -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,38804,-12243376] |
[a1,a2,a3,a4,a6] |
Generators |
[28740:948896:27] |
Generators of the group modulo torsion |
j |
24649793075727/261292936112 |
j-invariant |
L |
9.1471461199735 |
L(r)(E,1)/r! |
Ω |
0.17110577943287 |
Real period |
R |
6.6823766491273 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998579 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69056j1 17264c1 |
Quadratic twists by: -4 8 |