Atkin-Lehner |
2- 3+ 7- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
70224br |
Isogeny class |
Conductor |
70224 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
3483648 |
Modular degree for the optimal curve |
Δ |
7291255399737458688 = 226 · 39 · 74 · 112 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- 11+ 4 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15050288,-22467829824] |
[a1,a2,a3,a4,a6] |
Generators |
[32499720:6835096576:729] |
Generators of the group modulo torsion |
j |
92044580942235223464625/1780091650326528 |
j-invariant |
L |
5.3212724155331 |
L(r)(E,1)/r! |
Ω |
0.076650299047011 |
Real period |
R |
8.677840272033 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000122 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8778u1 |
Quadratic twists by: -4 |