Atkin-Lehner |
2- 3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072be |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
299520 |
Modular degree for the optimal curve |
Δ |
-297836474487552 = -1 · 28 · 319 · 7 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 4 7+ 11- 13- 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,16332,-209900] |
[a1,a2,a3,a4,a6] |
Generators |
[31780:564246:125] |
Generators of the group modulo torsion |
j |
2581513094144/1595917323 |
j-invariant |
L |
9.2111531335115 |
L(r)(E,1)/r! |
Ω |
0.31547373269839 |
Real period |
R |
3.6497306188878 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000042 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24024k1 |
Quadratic twists by: -3 |