Atkin-Lehner |
2+ 3- 89- |
Signs for the Atkin-Lehner involutions |
Class |
51264u |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-69665443282944 = -1 · 230 · 36 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 3 -4 -6 -2 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3444,393968] |
[a1,a2,a3,a4,a6] |
Generators |
[-726:14336:27] |
Generators of the group modulo torsion |
j |
23639903/364544 |
j-invariant |
L |
5.0963417185682 |
L(r)(E,1)/r! |
Ω |
0.45801212270386 |
Real period |
R |
2.7817722860888 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000092 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51264bl1 1602b1 5696b1 |
Quadratic twists by: -4 8 -3 |