Atkin-Lehner |
2- 3- 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
68076b |
Isogeny class |
Conductor |
68076 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-366372523443456 = -1 · 28 · 38 · 312 · 613 |
Discriminant |
Eigenvalues |
2- 3- -3 1 1 -1 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5079,-931394] |
[a1,a2,a3,a4,a6] |
Generators |
[27236:550467:64] |
Generators of the group modulo torsion |
j |
-77640952912/1963158669 |
j-invariant |
L |
5.7288850129971 |
L(r)(E,1)/r! |
Ω |
0.23266215806895 |
Real period |
R |
6.1557980254294 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000114 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22692e1 |
Quadratic twists by: -3 |