Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
3648r |
Isogeny class |
Conductor |
3648 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
141012366262272 = 238 · 33 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 4 -2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-22529,-1176993] |
[a1,a2,a3,a4,a6] |
Generators |
[-71:264:1] |
Generators of the group modulo torsion |
j |
4824238966273/537919488 |
j-invariant |
L |
3.797823553099 |
L(r)(E,1)/r! |
Ω |
0.39250754447514 |
Real period |
R |
3.2252658635113 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3648v1 114c1 10944bg1 91200v1 |
Quadratic twists by: -4 8 -3 5 |