Atkin-Lehner |
2+ 3+ 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
61710n |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
163840 |
Modular degree for the optimal curve |
Δ |
-29605760532480 = -1 · 216 · 3 · 5 · 116 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 11- 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9682,-454604] |
[a1,a2,a3,a4,a6] |
Generators |
[2126100:12652022:15625] |
Generators of the group modulo torsion |
j |
-56667352321/16711680 |
j-invariant |
L |
4.2397971544626 |
L(r)(E,1)/r! |
Ω |
0.23703822209389 |
Real period |
R |
8.9432774110011 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000166 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
510e1 |
Quadratic twists by: -11 |