Atkin-Lehner |
2+ 5+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
61370a |
Isogeny class |
Conductor |
61370 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8536320 |
Modular degree for the optimal curve |
Δ |
-3926599775079200 = -1 · 25 · 52 · 172 · 198 |
Discriminant |
Eigenvalues |
2+ 1 5+ 2 -3 2 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-759853024,8061931362766] |
[a1,a2,a3,a4,a6] |
Generators |
[1040275865042534:14756441311075499:61023377953] |
Generators of the group modulo torsion |
j |
-2856825358594046013529/231200 |
j-invariant |
L |
4.9922662436146 |
L(r)(E,1)/r! |
Ω |
0.16957436109391 |
Real period |
R |
22.079986965939 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
61370n1 |
Quadratic twists by: -19 |