Atkin-Lehner |
2+ 3- 5- 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030x |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-95088484820160 = -1 · 26 · 318 · 5 · 13 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- -1 -3 13- 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,9126,325620] |
[a1,a2,a3,a4,a6] |
Generators |
[84:1254:1] |
Generators of the group modulo torsion |
j |
115295088815711/130436879040 |
j-invariant |
L |
4.7490325789489 |
L(r)(E,1)/r! |
Ω |
0.39995611776415 |
Real period |
R |
2.9684710196934 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000045 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23010r1 |
Quadratic twists by: -3 |