Atkin-Lehner |
2- 5- 23- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
15410b |
Isogeny class |
Conductor |
15410 |
Conductor |
∏ cp |
182 |
Product of Tamagawa factors cp |
deg |
75712 |
Modular degree for the optimal curve |
Δ |
-22683520000000 = -1 · 213 · 57 · 232 · 67 |
Discriminant |
Eigenvalues |
2- -2 5- -3 -3 -2 -8 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-27430,1761252] |
[a1,a2,a3,a4,a6] |
Generators |
[-156:1578:1] [-116:1898:1] |
Generators of the group modulo torsion |
j |
-2282454477509562721/22683520000000 |
j-invariant |
L |
7.0802712131677 |
L(r)(E,1)/r! |
Ω |
0.68014601806221 |
Real period |
R |
0.057197407689283 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999981 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
123280k1 77050c1 |
Quadratic twists by: -4 5 |