Atkin-Lehner |
3+ 5+ 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
48675g |
Isogeny class |
Conductor |
48675 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
700416 |
Modular degree for the optimal curve |
Δ |
201261237890625 = 38 · 58 · 113 · 59 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -4 11- -2 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1023188,-398790844] |
[a1,a2,a3,a4,a6] |
Generators |
[-584:308:1] [1220:12452:1] |
Generators of the group modulo torsion |
j |
7581759897119792761/12880719225 |
j-invariant |
L |
4.7291254252996 |
L(r)(E,1)/r! |
Ω |
0.15011038444426 |
Real period |
R |
5.2507198206257 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9735j1 |
Quadratic twists by: 5 |