Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400bh |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
844800 |
Modular degree for the optimal curve |
Δ |
383384858906250000 = 24 · 317 · 510 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 1 -4 -4 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-429375,104115625] |
[a1,a2,a3,a4,a6] |
Generators |
[296:1719:1] [464:2187:1] |
Generators of the group modulo torsion |
j |
76857529600/3365793 |
j-invariant |
L |
10.409972159439 |
L(r)(E,1)/r! |
Ω |
0.29771030532434 |
Real period |
R |
8.7416961835808 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999746 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200cl1 22800v1 68400ci1 |
Quadratic twists by: -4 -3 5 |