Atkin-Lehner |
3- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
31713d |
Isogeny class |
Conductor |
31713 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
Δ |
4.999304898718E+26 |
Discriminant |
Eigenvalues |
1 3- -2 -2 11+ -4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-239746937,940342663505] |
[a1,a2,a3,a4,a6] |
Generators |
[-345195400457133:-87494953268396677:60098096213] |
Generators of the group modulo torsion |
j |
1717167849316307276617/563299624074237039 |
j-invariant |
L |
5.4918524612847 |
L(r)(E,1)/r! |
Ω |
0.048257997935179 |
Real period |
R |
18.966985426476 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95139i2 1023a2 |
Quadratic twists by: -3 -31 |