Atkin-Lehner |
3- 5+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
33135h |
Isogeny class |
Conductor |
33135 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
238464 |
Modular degree for the optimal curve |
Δ |
189983670173625 = 3 · 53 · 477 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 -4 -2 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-811854,-281622773] |
[a1,a2,a3,a4,a6] |
Generators |
[12836014976493643377607051514797793485705981281004727855:-5277575335620928195202796114546590269914070951647249709916:76114415158320906187448227893204375733302763021193] |
Generators of the group modulo torsion |
j |
5489965305721/17625 |
j-invariant |
L |
6.7404330579842 |
L(r)(E,1)/r! |
Ω |
0.15904873479436 |
Real period |
R |
84.759342055742 |
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 |
99405r1 705f1 |
Quadratic twists by: -3 -47 |