Atkin-Lehner |
2+ 3+ 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
31992b |
Isogeny class |
Conductor |
31992 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
107712 |
Modular degree for the optimal curve |
Δ |
-6985875558384 = -1 · 24 · 311 · 31 · 433 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 -3 6 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48072,4074885] |
[a1,a2,a3,a4,a6] |
Generators |
[130:75:1] |
Generators of the group modulo torsion |
j |
-767872893098576128/436617222399 |
j-invariant |
L |
5.1243050524813 |
L(r)(E,1)/r! |
Ω |
0.73791286882546 |
Real period |
R |
3.4721613275544 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63984o1 95976o1 |
Quadratic twists by: -4 -3 |