Atkin-Lehner |
2+ 3- 7+ 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
13398n |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
-2262011484348 = -1 · 22 · 38 · 7 · 114 · 292 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 11- 0 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1383,74902] |
[a1,a2,a3,a4,a6] |
Generators |
[-31:312:1] |
Generators of the group modulo torsion |
j |
-292239398603881/2262011484348 |
j-invariant |
L |
2.8360059763846 |
L(r)(E,1)/r! |
Ω |
0.70382398851549 |
Real period |
R |
0.12591953131485 |
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 |
107184bs1 40194bn1 93786s1 |
Quadratic twists by: -4 -3 -7 |