Atkin-Lehner |
3- 23- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
66309k |
Isogeny class |
Conductor |
66309 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
535680 |
Modular degree for the optimal curve |
Δ |
-12181842687769803 = -1 · 33 · 232 · 318 |
Discriminant |
Eigenvalues |
-2 3- 0 0 2 5 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,49652,3189016] |
[a1,a2,a3,a4,a6] |
Generators |
[320:7207:1] |
Generators of the group modulo torsion |
j |
15872000/14283 |
j-invariant |
L |
4.0571274297358 |
L(r)(E,1)/r! |
Ω |
0.26159217491569 |
Real period |
R |
0.86163115687063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000787 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
66309b1 |
Quadratic twists by: -31 |