Atkin-Lehner |
2- 3+ 5+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
31980b |
Isogeny class |
Conductor |
31980 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
25920 |
Modular degree for the optimal curve |
Δ |
-10775980800 = -1 · 28 · 35 · 52 · 132 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 4 -3 13- -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-221,-5079] |
[a1,a2,a3,a4,a6] |
Generators |
[31:130:1] |
Generators of the group modulo torsion |
j |
-4684079104/42093675 |
j-invariant |
L |
4.8875028518229 |
L(r)(E,1)/r! |
Ω |
0.54179755552721 |
Real period |
R |
0.75174186402936 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127920by1 95940h1 |
Quadratic twists by: -4 -3 |