Atkin-Lehner |
2- 3- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
84474bt |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
689472 |
Modular degree for the optimal curve |
Δ |
-1382942197698048 = -1 · 29 · 313 · 13 · 194 |
Discriminant |
Eigenvalues |
2- 3- 0 0 4 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-399695,97377815] |
[a1,a2,a3,a4,a6] |
Generators |
[351:-662:1] |
Generators of the group modulo torsion |
j |
-74330474937625/14556672 |
j-invariant |
L |
11.455869447405 |
L(r)(E,1)/r! |
Ω |
0.46676911755532 |
Real period |
R |
0.68174732170288 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000449 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28158f1 84474w1 |
Quadratic twists by: -3 -19 |