Atkin-Lehner |
2+ 3+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376b |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1155840 |
Modular degree for the optimal curve |
Δ |
-26491735862194176 = -1 · 212 · 310 · 78 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -5 -4 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1140589,469304389] |
[a1,a2,a3,a4,a6] |
Generators |
[595:-972:1] |
Generators of the group modulo torsion |
j |
-6949720863232/1121931 |
j-invariant |
L |
2.1363534412225 |
L(r)(E,1)/r! |
Ω |
0.36362181662983 |
Real period |
R |
1.468801748996 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001247 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89376o1 89376z1 |
Quadratic twists by: -4 -7 |