Atkin-Lehner |
3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
3393b |
Isogeny class |
Conductor |
3393 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
2240 |
Modular degree for the optimal curve |
Δ |
-290722419 = -1 · 33 · 135 · 29 |
Discriminant |
Eigenvalues |
2 3+ 3 0 6 13- -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-321,-2361] |
[a1,a2,a3,a4,a6] |
j |
-135479955456/10767497 |
j-invariant |
L |
5.6139595186707 |
L(r)(E,1)/r! |
Ω |
0.56139595186707 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54288z1 3393d1 84825b1 44109f1 |
Quadratic twists by: -4 -3 5 13 |