Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bu |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-9980928 = -1 · 210 · 33 · 192 |
Discriminant |
Eigenvalues |
2+ 3- -2 -3 0 5 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,51,-45] |
[a1,a2,a3,a4,a6] |
Generators |
[3:12:1] |
Generators of the group modulo torsion |
j |
38912/27 |
j-invariant |
L |
5.8548734267267 |
L(r)(E,1)/r! |
Ω |
1.295797156046 |
Real period |
R |
0.75305940691778 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996927 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312ct1 8664j1 69312e1 |
Quadratic twists by: -4 8 -19 |