Atkin-Lehner |
2+ 3+ 7- 103- |
Signs for the Atkin-Lehner involutions |
Class |
12978b |
Isogeny class |
Conductor |
12978 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1128960 |
Modular degree for the optimal curve |
Δ |
-747984866723136 = -1 · 26 · 39 · 78 · 103 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7- -2 1 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-238569639,1418368692797] |
[a1,a2,a3,a4,a6] |
Generators |
[8918:-4431:1] |
Generators of the group modulo torsion |
j |
-76291813922458084261302627/38001568192 |
j-invariant |
L |
3.7729162652211 |
L(r)(E,1)/r! |
Ω |
0.21542642614253 |
Real period |
R |
0.54730348267558 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
103824w1 12978s1 90846k1 |
Quadratic twists by: -4 -3 -7 |