Atkin-Lehner |
2- 3+ 31+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
123504u |
Isogeny class |
Conductor |
123504 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
705024 |
Modular degree for the optimal curve |
Δ |
3982486413508608 = 229 · 3 · 313 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 3 0 7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-64392,-5486352] |
[a1,a2,a3,a4,a6] |
Generators |
[1396772:31848448:2197] |
Generators of the group modulo torsion |
j |
7208854364036233/972286722048 |
j-invariant |
L |
9.0166731294354 |
L(r)(E,1)/r! |
Ω |
0.30237865544675 |
Real period |
R |
7.4547863933221 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999827137 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15438j1 |
Quadratic twists by: -4 |