Atkin-Lehner |
2- 53- |
Signs for the Atkin-Lehner involutions |
Class |
1696f |
Isogeny class |
Conductor |
1696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
112 |
Modular degree for the optimal curve |
Δ |
-27136 = -1 · 29 · 53 |
Discriminant |
Eigenvalues |
2- -2 1 -2 3 0 3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,0,-8] |
[a1,a2,a3,a4,a6] |
Generators |
[2:2:1] |
Generators of the group modulo torsion |
j |
-8/53 |
j-invariant |
L |
2.1621143163656 |
L(r)(E,1)/r! |
Ω |
1.7052071491361 |
Real period |
R |
0.63397409442629 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1696b1 3392b1 15264c1 42400a1 |
Quadratic twists by: -4 8 -3 5 |