Atkin-Lehner |
3+ 11+ 17+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
72369a |
Isogeny class |
Conductor |
72369 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
355968 |
Modular degree for the optimal curve |
Δ |
-13449717123830163 = -1 · 33 · 119 · 173 · 43 |
Discriminant |
Eigenvalues |
-1 3+ -2 0 11+ 4 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-8696,-5586298] |
[a1,a2,a3,a4,a6] |
Generators |
[29142:1743437:8] |
Generators of the group modulo torsion |
j |
-2693219311385091/498137671252969 |
j-invariant |
L |
3.2135802830095 |
L(r)(E,1)/r! |
Ω |
0.17718915618749 |
Real period |
R |
9.0682193868662 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001387 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72369f1 |
Quadratic twists by: -3 |