Atkin-Lehner |
2- 3- 5+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85140g |
Isogeny class |
Conductor |
85140 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1230336 |
Modular degree for the optimal curve |
Δ |
-2297733736994823600 = -1 · 24 · 324 · 52 · 11 · 432 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 11+ 4 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-234228,-84985823] |
[a1,a2,a3,a4,a6] |
Generators |
[1694:66177:1] |
Generators of the group modulo torsion |
j |
-121840769029881856/196993633144275 |
j-invariant |
L |
5.1391864320177 |
L(r)(E,1)/r! |
Ω |
0.1027432086503 |
Real period |
R |
4.1683099217581 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997933 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28380f1 |
Quadratic twists by: -3 |