Atkin-Lehner |
2+ 3- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
15624m |
Isogeny class |
Conductor |
15624 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
7168 |
Modular degree for the optimal curve |
Δ |
2604489552 = 24 · 37 · 74 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -4 2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-426,2329] |
[a1,a2,a3,a4,a6] |
Generators |
[5:18:1] |
Generators of the group modulo torsion |
j |
733001728/223293 |
j-invariant |
L |
4.1308303523276 |
L(r)(E,1)/r! |
Ω |
1.3364385995443 |
Real period |
R |
1.5454620787428 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
31248m1 124992co1 5208m1 109368v1 |
Quadratic twists by: -4 8 -3 -7 |