Atkin-Lehner |
2- 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776s |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
29859840 |
Modular degree for the optimal curve |
Δ |
1.5823497719595E+19 |
Discriminant |
Eigenvalues |
2- 2 -2 7- 0 -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8380101144,-295269028834576] |
[a1,a2,a3,a4,a6] |
Generators |
[-181568903297396061721883879998670248610740031514311814611431305071544279687591059775814674489965884350602759682034200174840840986980045302279033737877:-11337244685438170950634461743332427956210889029502588379479888544971566878186760026260185026224909687286039463638518004720297079765097662823130622:3435421735229920181924192826522942159451322164469203710872969818650757678847417413344650048359037695115140348084461234127823848070169284386841847] |
Generators of the group modulo torsion |
j |
135058930188560270934200713/32836306496 |
j-invariant |
L |
7.0784894878308 |
L(r)(E,1)/r! |
Ω |
0.015779282066295 |
Real period |
R |
224.29694386891 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8722j1 9968o1 |
Quadratic twists by: -4 -7 |