Atkin-Lehner |
2+ 3+ 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
57408c |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-21129024503808 = -1 · 226 · 34 · 132 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 -2 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1953,224289] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:468:1] |
Generators of the group modulo torsion |
j |
-3144219625/80600832 |
j-invariant |
L |
3.6540801112273 |
L(r)(E,1)/r! |
Ω |
0.570335514989 |
Real period |
R |
1.6017239041737 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000544 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408dd1 1794e1 |
Quadratic twists by: -4 8 |