Atkin-Lehner |
7- 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
47971h |
Isogeny class |
Conductor |
47971 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
3672 |
Modular degree for the optimal curve |
Δ |
-47971 = -1 · 72 · 11 · 89 |
Discriminant |
Eigenvalues |
0 0 -3 7- 11- 6 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-14,-23] |
[a1,a2,a3,a4,a6] |
Generators |
[25:123:1] |
Generators of the group modulo torsion |
j |
-6193152/979 |
j-invariant |
L |
4.0416517625477 |
L(r)(E,1)/r! |
Ω |
1.2234264112365 |
Real period |
R |
3.3035511784248 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999787 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47971b1 |
Quadratic twists by: -7 |