Atkin-Lehner |
2+ 3+ 7+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
98112d |
Isogeny class |
Conductor |
98112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-1404050407861248 = -1 · 210 · 37 · 76 · 732 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 4 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-30469,-2717627] |
[a1,a2,a3,a4,a6] |
Generators |
[24192435357:345014746328:74618461] |
Generators of the group modulo torsion |
j |
-3055009826357248/1371142976427 |
j-invariant |
L |
5.142436699008 |
L(r)(E,1)/r! |
Ω |
0.17683899534961 |
Real period |
R |
14.539883303106 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999754289 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
98112cc1 6132e1 |
Quadratic twists by: -4 8 |