Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304cw |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-7211150418640896 = -1 · 221 · 33 · 73 · 135 |
Discriminant |
Eigenvalues |
2+ 3- 1 7- -1 13+ 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,21215,-3901633] |
[a1,a2,a3,a4,a6] |
Generators |
[121:672:1] |
Generators of the group modulo torsion |
j |
11743520417/80199288 |
j-invariant |
L |
9.676135120905 |
L(r)(E,1)/r! |
Ω |
0.20878872677225 |
Real period |
R |
3.8620121260735 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999854515 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304ex1 3822g1 122304bs1 |
Quadratic twists by: -4 8 -7 |