Atkin-Lehner |
3+ 5+ 13+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
8385a |
Isogeny class |
Conductor |
8385 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
38400 |
Modular degree for the optimal curve |
Δ |
431123291015625 = 35 · 512 · 132 · 43 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 2 2 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-67926,6712074] |
[a1,a2,a3,a4,a6] |
Generators |
[336:4518:1] |
Generators of the group modulo torsion |
j |
34660293348948298849/431123291015625 |
j-invariant |
L |
2.3792352210995 |
L(r)(E,1)/r! |
Ω |
0.5315616468256 |
Real period |
R |
4.4759347016624 |
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 |
25155l1 41925l1 109005e1 |
Quadratic twists by: -3 5 13 |