Atkin-Lehner |
2+ 3- 7- 11+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
13398q |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-1315019284420165632 = -1 · 216 · 39 · 74 · 114 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-494050,144559028] |
[a1,a2,a3,a4,a6] |
Generators |
[28:11420:1] |
Generators of the group modulo torsion |
j |
-13336293950598670900633/1315019284420165632 |
j-invariant |
L |
4.8480986042484 |
L(r)(E,1)/r! |
Ω |
0.26487174979701 |
Real period |
R |
0.50843249903688 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
107184bm1 40194cb1 93786f1 |
Quadratic twists by: -4 -3 -7 |