Atkin-Lehner |
3+ 7- 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72471d |
Isogeny class |
Conductor |
72471 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-2225322717219 = -1 · 33 · 78 · 17 · 292 |
Discriminant |
Eigenvalues |
0 3+ -1 7- -1 -5 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-60041,-5643142] |
[a1,a2,a3,a4,a6] |
Generators |
[306:2131:1] [364:4538:1] |
Generators of the group modulo torsion |
j |
-203463474282496/18914931 |
j-invariant |
L |
6.8147147598278 |
L(r)(E,1)/r! |
Ω |
0.15249463145869 |
Real period |
R |
11.172056836876 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998946 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10353f1 |
Quadratic twists by: -7 |