Atkin-Lehner |
2- 3+ 5- 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
48360w |
Isogeny class |
Conductor |
48360 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
313344 |
Modular degree for the optimal curve |
Δ |
-2342437500000000 = -1 · 28 · 3 · 512 · 13 · 312 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 -4 13- -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8340,-2344188] |
[a1,a2,a3,a4,a6] |
Generators |
[218:2480:1] |
Generators of the group modulo torsion |
j |
-250630529348176/9150146484375 |
j-invariant |
L |
4.0128485020669 |
L(r)(E,1)/r! |
Ω |
0.20067269481992 |
Real period |
R |
3.3328305292046 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000063 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
96720x1 |
Quadratic twists by: -4 |