Atkin-Lehner |
2+ 3- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
65712m |
Isogeny class |
Conductor |
65712 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
93312 |
Modular degree for the optimal curve |
Δ |
-27592731648 = -1 · 210 · 39 · 372 |
Discriminant |
Eigenvalues |
2+ 3- -4 -1 2 -3 -8 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1640,26244] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:-216:1] [-26:228:1] |
Generators of the group modulo torsion |
j |
-348190276/19683 |
j-invariant |
L |
9.3208237877928 |
L(r)(E,1)/r! |
Ω |
1.1687880259448 |
Real period |
R |
0.22152158144652 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32856k1 65712l1 |
Quadratic twists by: -4 37 |