Atkin-Lehner |
2+ 3+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
124992j |
Isogeny class |
Conductor |
124992 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-949097253888 = -1 · 210 · 39 · 72 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7+ -4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,648,46440] |
[a1,a2,a3,a4,a6] |
Generators |
[1:217:1] |
Generators of the group modulo torsion |
j |
1492992/47089 |
j-invariant |
L |
3.6117003430842 |
L(r)(E,1)/r! |
Ω |
0.66480607822118 |
Real period |
R |
1.3581781869523 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999996874355 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
124992eg1 15624p1 124992i1 |
Quadratic twists by: -4 8 -3 |