Atkin-Lehner |
2+ 3+ 5- 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
68880m |
Isogeny class |
Conductor |
68880 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-378013440 = -1 · 28 · 3 · 5 · 74 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- 4 -6 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,140,640] |
[a1,a2,a3,a4,a6] |
Generators |
[32:192:1] |
Generators of the group modulo torsion |
j |
1176960944/1476615 |
j-invariant |
L |
6.7812207186099 |
L(r)(E,1)/r! |
Ω |
1.1362254954086 |
Real period |
R |
2.9840998756366 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992951 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34440w1 |
Quadratic twists by: -4 |