Atkin-Lehner |
2+ 7+ 19- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68894a |
Isogeny class |
Conductor |
68894 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
2193240 |
Modular degree for the optimal curve |
Δ |
-972202001983178624 = -1 · 27 · 78 · 19 · 375 |
Discriminant |
Eigenvalues |
2+ 3 2 7+ 2 6 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-326986,86278772] |
[a1,a2,a3,a4,a6] |
j |
-670698932263353/168644503424 |
j-invariant |
L |
6.6257117585718 |
L(r)(E,1)/r! |
Ω |
0.26502847075703 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
25 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68894c1 |
Quadratic twists by: -7 |