Atkin-Lehner |
3- 5+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
61605c |
Isogeny class |
Conductor |
61605 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
656640 |
Modular degree for the optimal curve |
Δ |
-648800047780846875 = -1 · 37 · 55 · 377 |
Discriminant |
Eigenvalues |
0 3- 5+ -2 -4 -5 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-16428,38762208] |
[a1,a2,a3,a4,a6] |
Generators |
[74:-6161:1] [-254:50117:8] |
Generators of the group modulo torsion |
j |
-262144/346875 |
j-invariant |
L |
6.8122741476948 |
L(r)(E,1)/r! |
Ω |
0.23202991310622 |
Real period |
R |
1.8349665719055 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999735 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20535e1 1665e1 |
Quadratic twists by: -3 37 |