Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696dt |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1419264 |
Modular degree for the optimal curve |
Δ |
-7680866267086848 = -1 · 214 · 37 · 118 |
Discriminant |
Eigenvalues |
2+ 3- -4 -5 11- 2 -4 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-894432,-325615840] |
[a1,a2,a3,a4,a6] |
Generators |
[1369:31869:1] |
Generators of the group modulo torsion |
j |
-30908416/3 |
j-invariant |
L |
1.9201075044267 |
L(r)(E,1)/r! |
Ω |
0.077621172357689 |
Real period |
R |
6.1842260510795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999978524 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696hd1 4356l1 23232bd1 69696ds1 |
Quadratic twists by: -4 8 -3 -11 |