Atkin-Lehner |
2- 3+ 5- 13+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
28470m |
Isogeny class |
Conductor |
28470 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
60480 |
Modular degree for the optimal curve |
Δ |
-177652800000 = -1 · 29 · 32 · 55 · 132 · 73 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 -4 13+ -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1860,36165] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:-247:1] [-47:173:1] |
Generators of the group modulo torsion |
j |
-711667507775041/177652800000 |
j-invariant |
L |
9.6521252930425 |
L(r)(E,1)/r! |
Ω |
0.96583103581128 |
Real period |
R |
0.055519978450096 |
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 |
85410d1 |
Quadratic twists by: -3 |