Atkin-Lehner |
3- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
74727m |
Isogeny class |
Conductor |
74727 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-182353489797540771 = -1 · 36 · 197 · 234 |
Discriminant |
Eigenvalues |
0 3- 1 -5 1 0 7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,60648,19724769] |
[a1,a2,a3,a4,a6] |
Generators |
[29545:859298:125] |
Generators of the group modulo torsion |
j |
719323136/5316979 |
j-invariant |
L |
4.3187246009365 |
L(r)(E,1)/r! |
Ω |
0.23310555310668 |
Real period |
R |
2.3158632118741 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003589 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8303a1 3933d1 |
Quadratic twists by: -3 -19 |