Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376u |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
75866112 |
Modular degree for the optimal curve |
Δ |
-9.6803022875889E+27 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 2 -2 -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-607527790,-7458602348716] |
[a1,a2,a3,a4,a6] |
Generators |
[4342570:456983262:125] |
Generators of the group modulo torsion |
j |
-3293471763919519109730496/1285643934445484858643 |
j-invariant |
L |
4.9306295889817 |
L(r)(E,1)/r! |
Ω |
0.014916436722313 |
Real period |
R |
11.805360577476 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999917196 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
89376cd1 12768d1 |
Quadratic twists by: -4 -7 |