Atkin-Lehner |
2+ 3+ 5+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160c |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
277954560 |
Modular degree for the optimal curve |
Δ |
-7.9193689238939E+30 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 6 -2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-57260640641,-5275625003167359] |
[a1,a2,a3,a4,a6] |
Generators |
[83734569431089081340066509269960562916352249015311683240352270560055699861376825872010158610222230588880224519746215665202176828854901157883837707271015813481850625826216217993696977828184598464463519:17432482244335597370777353874118318028779957708513893297007972254531196421845936679144814465781439218566576024119798427078956226587636493696335578215909822282508300829596008457336537064872650865471651840:282421592456763631671401913310208549848640006080614015042559523530039239493817103273598033686424696101220141835178899065501974830106089473815065286691368082696335161052450320894647997051552463359] |
Generators of the group modulo torsion |
j |
-79204963502810190656794906124641/30209994979453807519334400 |
j-invariant |
L |
5.7735791552423 |
L(r)(E,1)/r! |
Ω |
0.004879727519079 |
Real period |
R |
295.79413669455 |
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 |
68160da1 2130n1 |
Quadratic twists by: -4 8 |