Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ca |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1622016 |
Modular degree for the optimal curve |
Δ |
-1.3272536909526E+19 |
Discriminant |
Eigenvalues |
2+ 3- -1 4 11- 5 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-942348,393315824] |
[a1,a2,a3,a4,a6] |
Generators |
[542:6464:1] |
Generators of the group modulo torsion |
j |
-2259169/324 |
j-invariant |
L |
7.2094685153911 |
L(r)(E,1)/r! |
Ω |
0.21649550548369 |
Real period |
R |
4.1625971048891 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000843 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696gg1 2178d1 23232l1 69696cc1 |
Quadratic twists by: -4 8 -3 -11 |