Atkin-Lehner |
2+ 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
121680d |
Isogeny class |
Conductor |
121680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-2168588747520 = -1 · 28 · 33 · 5 · 137 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 3 -5 13+ 3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2028,-79092] |
[a1,a2,a3,a4,a6] |
Generators |
[546:2535:8] |
Generators of the group modulo torsion |
j |
-27648/65 |
j-invariant |
L |
5.9438453845802 |
L(r)(E,1)/r! |
Ω |
0.33215158167118 |
Real period |
R |
2.2368722876 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000063928 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60840a1 121680i1 9360f1 |
Quadratic twists by: -4 -3 13 |