Atkin-Lehner |
2+ 3+ 5+ 13- 73- |
Signs for the Atkin-Lehner involutions |
Class |
85410a |
Isogeny class |
Conductor |
85410 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
40320 |
Modular degree for the optimal curve |
Δ |
-852733440 = -1 · 29 · 33 · 5 · 132 · 73 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 3 0 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-390,3380] |
[a1,a2,a3,a4,a6] |
Generators |
[13:13:1] |
Generators of the group modulo torsion |
j |
-243321230907/31582720 |
j-invariant |
L |
5.345506736815 |
L(r)(E,1)/r! |
Ω |
1.5342158650253 |
Real period |
R |
0.87104866643132 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007151 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85410r1 |
Quadratic twists by: -3 |