Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cs |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
119808 |
Modular degree for the optimal curve |
Δ |
-2357455269888 = -1 · 212 · 313 · 192 |
Discriminant |
Eigenvalues |
2- 3+ -2 -1 0 -5 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6409,-208727] |
[a1,a2,a3,a4,a6] |
Generators |
[96:227:1] |
Generators of the group modulo torsion |
j |
-19692240832/1594323 |
j-invariant |
L |
2.6342396770694 |
L(r)(E,1)/r! |
Ω |
0.26555662794879 |
Real period |
R |
4.9598454705262 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001782 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312dq1 34656q1 69312dc1 |
Quadratic twists by: -4 8 -19 |