Atkin-Lehner |
2+ 3- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
12342m |
Isogeny class |
Conductor |
12342 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
177408 |
Modular degree for the optimal curve |
Δ |
-247887957416685696 = -1 · 27 · 312 · 118 · 17 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 11- -4 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,53600,23477870] |
[a1,a2,a3,a4,a6] |
Generators |
[334:8702:1] |
Generators of the group modulo torsion |
j |
79448965607/1156415616 |
j-invariant |
L |
2.9759243230373 |
L(r)(E,1)/r! |
Ω |
0.23139485132213 |
Real period |
R |
3.2152015332597 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
98736cb1 37026bo1 12342bg1 |
Quadratic twists by: -4 -3 -11 |