Atkin-Lehner |
3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
24321f |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
53856 |
Modular degree for the optimal curve |
Δ |
-8660313151281 = -1 · 32 · 118 · 672 |
Discriminant |
Eigenvalues |
-1 3+ -3 0 11- 3 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-9622,385892] |
[a1,a2,a3,a4,a6] |
Generators |
[50:-207:1] [65:168:1] |
Generators of the group modulo torsion |
j |
-459601153/40401 |
j-invariant |
L |
3.8301785672006 |
L(r)(E,1)/r! |
Ω |
0.71765756583183 |
Real period |
R |
0.44475466080652 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72963k1 24321d1 |
Quadratic twists by: -3 -11 |