Atkin-Lehner |
2- 3- 5- 17- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
23970w |
Isogeny class |
Conductor |
23970 |
Conductor |
∏ cp |
1536 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-333786357882720000 = -1 · 28 · 312 · 54 · 174 · 47 |
Discriminant |
Eigenvalues |
2- 3- 5- 0 0 -2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1123020,458816400] |
[a1,a2,a3,a4,a6] |
Generators |
[720:4500:1] |
Generators of the group modulo torsion |
j |
-156634061220235043455681/333786357882720000 |
j-invariant |
L |
10.434116991568 |
L(r)(E,1)/r! |
Ω |
0.30480867791345 |
Real period |
R |
0.35658013218714 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
71910d1 119850b1 |
Quadratic twists by: -3 5 |