Atkin-Lehner |
2+ 3+ 7+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
32214d |
Isogeny class |
Conductor |
32214 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-1219493184 = -1 · 26 · 3 · 72 · 133 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ -5 13- -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,137,1621] |
[a1,a2,a3,a4,a6] |
Generators |
[6:-55:1] [3:44:1] |
Generators of the group modulo torsion |
j |
281140102151/1219493184 |
j-invariant |
L |
4.9145138704994 |
L(r)(E,1)/r! |
Ω |
1.0988103023882 |
Real period |
R |
0.37271476400562 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96642bz1 |
Quadratic twists by: -3 |