Atkin-Lehner |
3+ 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
45123c |
Isogeny class |
Conductor |
45123 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
224640 |
Modular degree for the optimal curve |
Δ |
-4710362816918889 = -1 · 36 · 138 · 892 |
Discriminant |
Eigenvalues |
-1 3+ 3 -2 0 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,27966,-2756616] |
[a1,a2,a3,a4,a6] |
Generators |
[82:269:1] |
Generators of the group modulo torsion |
j |
2965288703/5774409 |
j-invariant |
L |
3.3916275075361 |
L(r)(E,1)/r! |
Ω |
0.22659427755807 |
Real period |
R |
3.7419606797965 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999389 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45123e1 |
Quadratic twists by: 13 |