Atkin-Lehner |
2- 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
30420a |
Isogeny class |
Conductor |
30420 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-6422411112577200 = -1 · 24 · 39 · 52 · 138 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -6 13+ -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,18252,3737097] |
[a1,a2,a3,a4,a6] |
Generators |
[-104:845:1] [52:-2197:1] |
Generators of the group modulo torsion |
j |
442368/4225 |
j-invariant |
L |
7.7562781200858 |
L(r)(E,1)/r! |
Ω |
0.31037424422586 |
Real period |
R |
2.082506915544 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
121680cf1 30420c1 2340d1 |
Quadratic twists by: -4 -3 13 |