Atkin-Lehner |
3+ 13+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
52221b |
Isogeny class |
Conductor |
52221 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-61250772647727 = -1 · 36 · 138 · 103 |
Discriminant |
Eigenvalues |
1 3+ 4 1 -4 13+ -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-111543,-14390280] |
[a1,a2,a3,a4,a6] |
Generators |
[3392930278634922030:123872128833205045965:2336647128852392] |
Generators of the group modulo torsion |
j |
-188152476889/75087 |
j-invariant |
L |
7.66703875257 |
L(r)(E,1)/r! |
Ω |
0.13061651000365 |
Real period |
R |
29.349424327582 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52221c1 |
Quadratic twists by: 13 |