Atkin-Lehner |
2+ 3- 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
83904i |
Isogeny class |
Conductor |
83904 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-24744296448 = -1 · 221 · 33 · 19 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -2 4 -2 -3 5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-769,-11425] |
[a1,a2,a3,a4,a6] |
Generators |
[43:192:1] |
Generators of the group modulo torsion |
j |
-192100033/94392 |
j-invariant |
L |
7.9900265737321 |
L(r)(E,1)/r! |
Ω |
0.44289961438376 |
Real period |
R |
1.5033554464441 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004493 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83904bj1 2622c1 |
Quadratic twists by: -4 8 |