Atkin-Lehner |
2- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712cy |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-35428932517888 = -1 · 220 · 7 · 136 |
Discriminant |
Eigenvalues |
2- -2 0 7- 0 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5633,-331265] |
[a1,a2,a3,a4,a6] |
Generators |
[498861:9444352:1331] |
Generators of the group modulo torsion |
j |
-15625/28 |
j-invariant |
L |
4.3791872967764 |
L(r)(E,1)/r! |
Ω |
0.25995021908605 |
Real period |
R |
8.4231267631824 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004153 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
75712h1 18928z1 448f1 |
Quadratic twists by: -4 8 13 |