Atkin-Lehner |
2- 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
69776g |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
435456 |
Modular degree for the optimal curve |
Δ |
-1075980091260928 = -1 · 221 · 78 · 89 |
Discriminant |
Eigenvalues |
2- -2 -4 7+ 3 -2 5 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,12920,-1469196] |
[a1,a2,a3,a4,a6] |
Generators |
[702:18816:1] |
Generators of the group modulo torsion |
j |
10100279/45568 |
j-invariant |
L |
3.3125242605906 |
L(r)(E,1)/r! |
Ω |
0.24777506847555 |
Real period |
R |
1.1140898484953 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999957869 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8722a1 69776t1 |
Quadratic twists by: -4 -7 |