Atkin-Lehner |
2+ 7+ 19+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
39368a |
Isogeny class |
Conductor |
39368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-18351978525943552 = -1 · 28 · 710 · 193 · 37 |
Discriminant |
Eigenvalues |
2+ 0 0 7+ 0 -2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,62185,2618506] |
[a1,a2,a3,a4,a6] |
Generators |
[57712639665:-4282431835456:10503459] |
Generators of the group modulo torsion |
j |
103882086222462000/71687416116967 |
j-invariant |
L |
4.5806590116636 |
L(r)(E,1)/r! |
Ω |
0.24470844066751 |
Real period |
R |
18.718843531386 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78736c1 |
Quadratic twists by: -4 |