Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696dc |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3041280 |
Modular degree for the optimal curve |
Δ |
-3.8746418816906E+21 |
Discriminant |
Eigenvalues |
2+ 3- 3 -2 11- -1 -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1489389,2911977772] |
[a1,a2,a3,a4,a6] |
Generators |
[-259163608:21960170694:493039] |
Generators of the group modulo torsion |
j |
36534162368/387420489 |
j-invariant |
L |
7.4861268698532 |
L(r)(E,1)/r! |
Ω |
0.10266120021146 |
Real period |
R |
12.153450466375 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696cz1 34848ci1 23232cj1 69696cy1 |
Quadratic twists by: -4 8 -3 -11 |