Atkin-Lehner |
2+ 3- 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936i |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
141312 |
Modular degree for the optimal curve |
Δ |
-20933363040624 = -1 · 24 · 32 · 313 · 474 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 0 6 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,3304,208743] |
[a1,a2,a3,a4,a6] |
Generators |
[3481:205437:1] |
Generators of the group modulo torsion |
j |
249225452807936/1308335190039 |
j-invariant |
L |
8.7063160487661 |
L(r)(E,1)/r! |
Ω |
0.49095668894088 |
Real period |
R |
1.4777807364757 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000502 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34968f1 |
Quadratic twists by: -4 |