Atkin-Lehner |
2+ 3+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31248f |
Isogeny class |
Conductor |
31248 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
17408 |
Modular degree for the optimal curve |
Δ |
-4115736576 = -1 · 211 · 33 · 74 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- -1 1 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-699,7754] |
[a1,a2,a3,a4,a6] |
Generators |
[17:28:1] [-23:108:1] |
Generators of the group modulo torsion |
j |
-683064198/74431 |
j-invariant |
L |
7.4923663697159 |
L(r)(E,1)/r! |
Ω |
1.3512860933304 |
Real period |
R |
0.17326933963817 |
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 |
15624q1 124992dx1 31248e1 |
Quadratic twists by: -4 8 -3 |