Atkin-Lehner |
2- 3- 7+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31122w |
Isogeny class |
Conductor |
31122 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
983040 |
Modular degree for the optimal curve |
Δ |
38646899310329856 = 220 · 310 · 7 · 13 · 193 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ 0 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9482639,11241735383] |
[a1,a2,a3,a4,a6] |
Generators |
[1011:51334:1] |
Generators of the group modulo torsion |
j |
129355170662787770927017/53013579300864 |
j-invariant |
L |
9.5111711275954 |
L(r)(E,1)/r! |
Ω |
0.29597037872377 |
Real period |
R |
1.6067775377738 |
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 |
10374d1 |
Quadratic twists by: -3 |