Atkin-Lehner |
2+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
21824d |
Isogeny class |
Conductor |
21824 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
211200 |
Modular degree for the optimal curve |
Δ |
-157216615333888 = -1 · 215 · 115 · 313 |
Discriminant |
Eigenvalues |
2+ 2 0 -1 11+ -4 7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1414753,-647221695] |
[a1,a2,a3,a4,a6] |
Generators |
[132905073222827635231433092725201:4356706637511208524289804499064084:67677301979064516612273861187] |
Generators of the group modulo torsion |
j |
-9556876080347597000/4797870341 |
j-invariant |
L |
7.1216011506991 |
L(r)(E,1)/r! |
Ω |
0.069214863135786 |
Real period |
R |
51.44560595842 |
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 |
21824o1 10912f1 |
Quadratic twists by: -4 8 |