Atkin-Lehner |
2- 5+ 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
51520bq |
Isogeny class |
Conductor |
51520 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1152000 |
Modular degree for the optimal curve |
Δ |
-455214233600000 = -1 · 214 · 55 · 75 · 232 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- 1 -5 -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8286181,9183545981] |
[a1,a2,a3,a4,a6] |
Generators |
[1660:161:1] |
Generators of the group modulo torsion |
j |
-3840316976122235063296/27784071875 |
j-invariant |
L |
3.3095168637037 |
L(r)(E,1)/r! |
Ω |
0.36329065317959 |
Real period |
R |
0.91098321268474 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999544 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51520g1 12880g1 |
Quadratic twists by: -4 8 |