Atkin-Lehner |
5+ 31+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
31775c |
Isogeny class |
Conductor |
31775 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-20355859375 = -1 · 58 · 31 · 412 |
Discriminant |
Eigenvalues |
-1 -2 5+ -4 -6 4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,62,6867] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:69:1] [7:84:1] |
Generators of the group modulo torsion |
j |
1685159/1302775 |
j-invariant |
L |
3.1348717167371 |
L(r)(E,1)/r! |
Ω |
0.94795483013817 |
Real period |
R |
1.653492137531 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6355c1 |
Quadratic twists by: 5 |