Atkin-Lehner |
2+ 3+ 11+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
15312a |
Isogeny class |
Conductor |
15312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
274560 |
Modular degree for the optimal curve |
Δ |
-1425020702331561984 = -1 · 211 · 311 · 115 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ 3 1 11+ 3 -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1713904,866109472] |
[a1,a2,a3,a4,a6] |
Generators |
[644:5388:1] |
Generators of the group modulo torsion |
j |
-271865119154793108194/695810889810333 |
j-invariant |
L |
5.4018917587083 |
L(r)(E,1)/r! |
Ω |
0.27039131084107 |
Real period |
R |
4.9945130835614 |
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 |
7656h1 61248cn1 45936t1 |
Quadratic twists by: -4 8 -3 |