Atkin-Lehner |
2- 3+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bd |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
28672 |
Modular degree for the optimal curve |
Δ |
-52310016 = -1 · 212 · 33 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3+ -3 -5 11+ -6 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,21,346] |
[a1,a2,a3,a4,a6] |
Generators |
[5:-24:1] [-3:16:1] |
Generators of the group modulo torsion |
j |
9261/473 |
j-invariant |
L |
6.8807377893378 |
L(r)(E,1)/r! |
Ω |
1.5171859652228 |
Real period |
R |
0.5668996704293 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000028 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4257d1 68112bi1 |
Quadratic twists by: -4 -3 |