Atkin-Lehner |
2+ 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
69056j |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
24 |
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 |
[120:4316:1] |
Generators of the group modulo torsion |
j |
24649793075727/261292936112 |
j-invariant |
L |
2.7051897369266 |
L(r)(E,1)/r! |
Ω |
0.25553408757922 |
Real period |
R |
0.44110059875254 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000509 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69056o1 2158c1 |
Quadratic twists by: -4 8 |