Atkin-Lehner |
3+ 5+ 29+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
48285a |
Isogeny class |
Conductor |
48285 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-440725798834824375 = -1 · 39 · 54 · 294 · 373 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 4 0 2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-160733,-40399748] |
[a1,a2,a3,a4,a6] |
Generators |
[1532432541122:-455875887960163:17373979] |
Generators of the group modulo torsion |
j |
-23331627739527723/22391190308125 |
j-invariant |
L |
4.0216377744925 |
L(r)(E,1)/r! |
Ω |
0.11472572632786 |
Real period |
R |
17.527183759103 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48285b1 |
Quadratic twists by: -3 |