Atkin-Lehner |
3+ 7+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
12369c |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
4352 |
Modular degree for the optimal curve |
Δ |
-27051003 = -1 · 38 · 7 · 19 · 31 |
Discriminant |
Eigenvalues |
-2 3+ 0 7+ -4 0 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-78,-340] |
[a1,a2,a3,a4,a6] |
Generators |
[11:3:1] [15:40:1] |
Generators of the group modulo torsion |
j |
-53157376000/27051003 |
j-invariant |
L |
2.9789810635507 |
L(r)(E,1)/r! |
Ω |
0.78354036678173 |
Real period |
R |
1.9009748507183 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37107g1 86583y1 |
Quadratic twists by: -3 -7 |