Atkin-Lehner |
2+ 3- 5+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
40050q |
Isogeny class |
Conductor |
40050 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
5308416 |
Modular degree for the optimal curve |
Δ |
3448042352100000000 = 28 · 318 · 58 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 4 0 4 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-221704542,-1270547931884] |
[a1,a2,a3,a4,a6] |
Generators |
[6808666574702724908484:171037017859731985440758:389322431600357871] |
Generators of the group modulo torsion |
j |
105803474625631920221209/302708793600 |
j-invariant |
L |
5.2225460474745 |
L(r)(E,1)/r! |
Ω |
0.03912514022206 |
Real period |
R |
33.370781662601 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999997 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13350l1 8010n1 |
Quadratic twists by: -3 5 |