Atkin-Lehner |
3+ 7- 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
12243d |
Isogeny class |
Conductor |
12243 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-1049237343 = -1 · 32 · 73 · 112 · 532 |
Discriminant |
Eigenvalues |
-1 3+ -4 7- 11- 4 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-130,-1714] |
[a1,a2,a3,a4,a6] |
Generators |
[26:102:1] |
Generators of the group modulo torsion |
j |
-243087455521/1049237343 |
j-invariant |
L |
1.9644497579005 |
L(r)(E,1)/r! |
Ω |
0.64275935180768 |
Real period |
R |
0.50937927556032 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36729v1 85701bc1 |
Quadratic twists by: -3 -7 |