Atkin-Lehner |
3- 7+ 37- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
31857c |
Isogeny class |
Conductor |
31857 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
49536 |
Modular degree for the optimal curve |
Δ |
968266786977 = 33 · 73 · 37 · 414 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 0 2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-7699,-256312] |
[a1,a2,a3,a4,a6] |
Generators |
[113:509:1] |
Generators of the group modulo torsion |
j |
50469638798675377/968266786977 |
j-invariant |
L |
3.3407794174739 |
L(r)(E,1)/r! |
Ω |
0.51026618074175 |
Real period |
R |
4.3647538527412 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95571f1 |
Quadratic twists by: -3 |