Atkin-Lehner |
2- 3+ 5+ 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69090bf |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
Δ |
1227964378725000000 = 26 · 33 · 58 · 77 · 472 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -2 4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3131101,-2133161101] |
[a1,a2,a3,a4,a6] |
Generators |
[-1019:1308:1] |
Generators of the group modulo torsion |
j |
28855374247604721601/10437525000000 |
j-invariant |
L |
8.7241762788513 |
L(r)(E,1)/r! |
Ω |
0.11349708629516 |
Real period |
R |
3.2027901050427 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000408 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9870u2 |
Quadratic twists by: -7 |