Atkin-Lehner |
2+ 5+ 7+ 11+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
111650d |
Isogeny class |
Conductor |
111650 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2032128 |
Modular degree for the optimal curve |
Δ |
-6481339536179200 = -1 · 216 · 52 · 7 · 117 · 29 |
Discriminant |
Eigenvalues |
2+ 2 5+ 7+ 11+ -1 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1972985,1065864485] |
[a1,a2,a3,a4,a6] |
Generators |
[2172566:61310261:1331] |
Generators of the group modulo torsion |
j |
-33974681788624700123905/259253581447168 |
j-invariant |
L |
6.8986989277643 |
L(r)(E,1)/r! |
Ω |
0.37894215419815 |
Real period |
R |
9.1025752201056 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000355 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111650w1 |
Quadratic twists by: 5 |