Atkin-Lehner |
2+ 3+ 23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344c |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
15049216 |
Modular degree for the optimal curve |
Δ |
-3.6538450979906E+23 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -2 0 2 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-172158356,-869870198592] |
[a1,a2,a3,a4,a6] |
Generators |
[132039287605708670718045571783168493629559983641079060205630180532023835652639651255658221905718244246435595:15065395634259945121835294978517249236857365401455138080176449295126416970745684899706480515228545815077079702:5887835845046906501634447296852536184084785479201166334610170226990798206637979308309682834621367283875] |
Generators of the group modulo torsion |
j |
-2204286646259029699004056144/1427283241402563974727 |
j-invariant |
L |
6.9189193926611 |
L(r)(E,1)/r! |
Ω |
0.020838702116718 |
Real period |
R |
166.01128404993 |
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 |
33672h1 |
Quadratic twists by: -4 |