Atkin-Lehner |
2+ 3- 43- |
Signs for the Atkin-Lehner involutions |
Class |
24768bi |
Isogeny class |
Conductor |
24768 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
337920 |
Modular degree for the optimal curve |
Δ |
-1215020434649357376 = -1 · 26 · 317 · 435 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 1 -3 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1485219,-698696444] |
[a1,a2,a3,a4,a6] |
Generators |
[15212:1869984:1] |
Generators of the group modulo torsion |
j |
-7765826776893057088/26042104652121 |
j-invariant |
L |
3.8062333979096 |
L(r)(E,1)/r! |
Ω |
0.068365144710065 |
Real period |
R |
5.5675058014603 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24768t1 12384g1 8256x1 |
Quadratic twists by: -4 8 -3 |