Atkin-Lehner |
2+ 3- 5- 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
32370m |
Isogeny class |
Conductor |
32370 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
268800 |
Modular degree for the optimal curve |
Δ |
-13983840000000000 = -1 · 214 · 34 · 510 · 13 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 2 13- -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-131513,19207388] |
[a1,a2,a3,a4,a6] |
Generators |
[204:-1040:1] |
Generators of the group modulo torsion |
j |
-251550404111151217801/13983840000000000 |
j-invariant |
L |
5.383886146347 |
L(r)(E,1)/r! |
Ω |
0.39125597674245 |
Real period |
R |
0.6880260579241 |
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 |
97110ce1 |
Quadratic twists by: -3 |