Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
33212a |
Isogeny class |
Conductor |
33212 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
129600 |
Modular degree for the optimal curve |
Δ |
-6249951199088 = -1 · 24 · 198 · 23 |
Discriminant |
Eigenvalues |
2- 1 -4 -2 -6 3 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32610,-2280691] |
[a1,a2,a3,a4,a6] |
Generators |
[6735:61381:27] |
Generators of the group modulo torsion |
j |
-5095042816/8303 |
j-invariant |
L |
2.8655972383535 |
L(r)(E,1)/r! |
Ω |
0.17761855355956 |
Real period |
R |
8.0667170769208 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1748a1 |
Quadratic twists by: -19 |