Atkin-Lehner |
2+ 3+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744a |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7902720 |
Modular degree for the optimal curve |
Δ |
-3.9779016646619E+25 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 11+ 0 3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-36438033,-315025068735] |
[a1,a2,a3,a4,a6] |
Generators |
[3349129801665284626579551343724021951380547195818589873113:448148986951632688051810549032158459187390461130509583914012:163831221958453345970876297427229799764915871592543671] |
Generators of the group modulo torsion |
j |
-226591821421000000/1684650343696353 |
j-invariant |
L |
4.9533108990089 |
L(r)(E,1)/r! |
Ω |
0.027176919188237 |
Real period |
R |
91.130839089975 |
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 |
51744bb1 103488hb1 51744bg1 |
Quadratic twists by: -4 8 -7 |