Atkin-Lehner |
3+ 7+ 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
30597c |
Isogeny class |
Conductor |
30597 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
195552 |
Modular degree for the optimal curve |
Δ |
-162587941362651 = -1 · 3 · 77 · 313 · 472 |
Discriminant |
Eigenvalues |
-2 3+ 1 7+ -4 3 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-8330,682484] |
[a1,a2,a3,a4,a6] |
Generators |
[19:-729:1] |
Generators of the group modulo torsion |
j |
-63930904880214016/162587941362651 |
j-invariant |
L |
2.0284218651904 |
L(r)(E,1)/r! |
Ω |
0.50784918036379 |
Real period |
R |
0.66569037410452 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
91791c1 |
Quadratic twists by: -3 |