Atkin-Lehner |
2+ 3+ 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
21840d |
Isogeny class |
Conductor |
21840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
515970000 = 24 · 34 · 54 · 72 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- 0 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-132711,-18564210] |
[a1,a2,a3,a4,a6] |
Generators |
[11658:56924:27] |
Generators of the group modulo torsion |
j |
16155773913566746624/32248125 |
j-invariant |
L |
3.8463092013279 |
L(r)(E,1)/r! |
Ω |
0.25013389831831 |
Real period |
R |
7.68850049351 |
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 |
10920p1 87360hb1 65520bp1 109200bm1 |
Quadratic twists by: -4 8 -3 5 |