Atkin-Lehner |
2+ 5+ 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
4270a |
Isogeny class |
Conductor |
4270 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
8369200 = 24 · 52 · 73 · 61 |
Discriminant |
Eigenvalues |
2+ -3 5+ 7- -3 -6 -7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-70,196] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:18:1] [-7:21:1] |
Generators of the group modulo torsion |
j |
38238692409/8369200 |
j-invariant |
L |
2.278332997793 |
L(r)(E,1)/r! |
Ω |
2.1955378194789 |
Real period |
R |
0.086475888260783 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34160m1 38430bq1 21350q1 29890j1 |
Quadratic twists by: -4 -3 5 -7 |