Atkin-Lehner |
2- 3- 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544dn |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
229376 |
Modular degree for the optimal curve |
Δ |
-370361438862912 = -1 · 26 · 310 · 78 · 17 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ 4 2 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,9321,-858688] |
[a1,a2,a3,a4,a6] |
Generators |
[46562249404:-622004236490:302111711] |
Generators of the group modulo torsion |
j |
1919569026752/7938130977 |
j-invariant |
L |
7.9033507780744 |
L(r)(E,1)/r! |
Ω |
0.27160028421968 |
Real period |
R |
14.549599607788 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000707 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544el1 34272j2 22848bz1 |
Quadratic twists by: -4 8 -3 |