Atkin-Lehner |
3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825a |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-138625449046875 = -1 · 34 · 56 · 78 · 19 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7+ -3 -2 7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-11433,-732607] |
[a1,a2,a3,a4,a6] |
Generators |
[327:-5513:1] |
Generators of the group modulo torsion |
j |
-1835008/1539 |
j-invariant |
L |
3.6130367354729 |
L(r)(E,1)/r! |
Ω |
0.22294110354188 |
Real period |
R |
0.67525994489801 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001208 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2793g1 69825bt1 |
Quadratic twists by: 5 -7 |