Atkin-Lehner |
2- 3+ 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
57330dc |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
94276356475392000 = 212 · 33 · 53 · 79 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -6 13+ 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-172073,-23120919] |
[a1,a2,a3,a4,a6] |
Generators |
[-229:2172:1] |
Generators of the group modulo torsion |
j |
177381177331203/29679104000 |
j-invariant |
L |
7.8493986377029 |
L(r)(E,1)/r! |
Ω |
0.23707424388896 |
Real period |
R |
0.68978027980002 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000145 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57330j3 8190bf1 |
Quadratic twists by: -3 -7 |