Atkin-Lehner |
2- 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360cc |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
81920 |
Modular degree for the optimal curve |
Δ |
-1483012239360 = -1 · 212 · 3 · 5 · 176 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -4 -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-96,-58560] |
[a1,a2,a3,a4,a6] |
Generators |
[74:-578:1] [1064:34688:1] |
Generators of the group modulo torsion |
j |
-1/15 |
j-invariant |
L |
8.2098686128374 |
L(r)(E,1)/r! |
Ω |
0.38714560505412 |
Real period |
R |
5.3015380425609 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000023 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4335d1 240d1 |
Quadratic twists by: -4 17 |