Atkin-Lehner |
3- 5+ 7+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
69615h |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
-141510714447375 = -1 · 316 · 53 · 7 · 13 · 172 |
Discriminant |
Eigenvalues |
1 3- 5+ 7+ 6 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-10260,-695709] |
[a1,a2,a3,a4,a6] |
Generators |
[656047470:-69315924911:59319] |
Generators of the group modulo torsion |
j |
-163855897047361/194116206375 |
j-invariant |
L |
7.5517916453052 |
L(r)(E,1)/r! |
Ω |
0.22686200884055 |
Real period |
R |
16.644020046605 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205k1 |
Quadratic twists by: -3 |