Atkin-Lehner |
2+ 3+ 17+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
72624c |
Isogeny class |
Conductor |
72624 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
915840 |
Modular degree for the optimal curve |
Δ |
-137797215083490048 = -1 · 28 · 3 · 1710 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -4 -2 -2 0 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-147865,-28198379] |
[a1,a2,a3,a4,a6] |
Generators |
[715095372:9880784863:1295029] |
Generators of the group modulo torsion |
j |
-1396634760092363776/538270371419883 |
j-invariant |
L |
2.1424162030739 |
L(r)(E,1)/r! |
Ω |
0.1194477666926 |
Real period |
R |
8.9680044374884 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980367 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36312c1 |
Quadratic twists by: -4 |