Atkin-Lehner |
3+ 5+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
27495a |
Isogeny class |
Conductor |
27495 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
68352 |
Modular degree for the optimal curve |
Δ |
-189296630859375 = -1 · 33 · 512 · 13 · 472 |
Discriminant |
Eigenvalues |
1 3+ 5+ 2 4 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-13830,914551] |
[a1,a2,a3,a4,a6] |
Generators |
[1510:17137:8] |
Generators of the group modulo torsion |
j |
-10835380130672187/7010986328125 |
j-invariant |
L |
6.5490207279604 |
L(r)(E,1)/r! |
Ω |
0.52413743236883 |
Real period |
R |
6.2474270329847 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27495d1 |
Quadratic twists by: -3 |