Atkin-Lehner |
3+ 11- 17- 43- |
Signs for the Atkin-Lehner involutions |
Class |
72369h |
Isogeny class |
Conductor |
72369 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
337920 |
Modular degree for the optimal curve |
Δ |
-83512161513 = -1 · 33 · 114 · 173 · 43 |
Discriminant |
Eigenvalues |
-1 3+ 0 -4 11- -3 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-582830,171407550] |
[a1,a2,a3,a4,a6] |
Generators |
[-6530:84375:8] [11910:-5875:27] |
Generators of the group modulo torsion |
j |
-810932943631255171875/3093043019 |
j-invariant |
L |
5.9459905808519 |
L(r)(E,1)/r! |
Ω |
0.72304075858197 |
Real period |
R |
0.34264957348015 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999443 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72369c1 |
Quadratic twists by: -3 |