Atkin-Lehner |
3- 13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
80613g |
Isogeny class |
Conductor |
80613 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
677376 |
Modular degree for the optimal curve |
Δ |
-5302194405056523 = -1 · 313 · 137 · 53 |
Discriminant |
Eigenvalues |
-2 3- -2 -2 -3 13+ 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-249951,-48225798] |
[a1,a2,a3,a4,a6] |
Generators |
[641:7411:1] [884:-20534:1] |
Generators of the group modulo torsion |
j |
-490795651072/1506843 |
j-invariant |
L |
4.3221865861751 |
L(r)(E,1)/r! |
Ω |
0.10673970348154 |
Real period |
R |
5.0615966286348 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997829 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26871f1 6201c1 |
Quadratic twists by: -3 13 |