Atkin-Lehner |
2+ 3- 23- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
67344i |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
149760 |
Modular degree for the optimal curve |
Δ |
-11219302441728 = -1 · 28 · 310 · 233 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 0 -5 -3 -5 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4713,-205245] |
[a1,a2,a3,a4,a6] |
Generators |
[102:621:1] |
Generators of the group modulo torsion |
j |
-45234335104000/43825400163 |
j-invariant |
L |
4.9229701427748 |
L(r)(E,1)/r! |
Ω |
0.27716712339659 |
Real period |
R |
0.59205797110986 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001378 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33672e1 |
Quadratic twists by: -4 |