Atkin-Lehner |
3+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
1683d |
Isogeny class |
Conductor |
1683 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
864 |
Modular degree for the optimal curve |
Δ |
7571243097 = 39 · 113 · 172 |
Discriminant |
Eigenvalues |
-1 3+ -2 -2 11- -2 17- 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-596,3862] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:98:1] |
Generators of the group modulo torsion |
j |
1187648379/384659 |
j-invariant |
L |
1.5837387746094 |
L(r)(E,1)/r! |
Ω |
1.2178415785565 |
Real period |
R |
0.4334824283923 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
26928y1 107712g1 1683a1 42075h1 |
Quadratic twists by: -4 8 -3 5 |