Atkin-Lehner |
2- 3+ 5+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
28380a |
Isogeny class |
Conductor |
28380 |
Conductor |
∏ cp |
252 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
5577719416909200 = 24 · 32 · 52 · 117 · 433 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -3 11- 2 -8 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48966,2133441] |
[a1,a2,a3,a4,a6] |
Generators |
[-222:1419:1] [-24:-1815:1] |
Generators of the group modulo torsion |
j |
811514872476338944/348607463556825 |
j-invariant |
L |
6.3558468953957 |
L(r)(E,1)/r! |
Ω |
0.38604331134055 |
Real period |
R |
0.065333639836121 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
113520bj1 85140q1 |
Quadratic twists by: -4 -3 |