Atkin-Lehner |
2+ 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312n |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-1445373935616 = -1 · 224 · 3 · 13 · 472 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 0 13- 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7969,282529] |
[a1,a2,a3,a4,a6] |
j |
-213525509833/5513664 |
j-invariant |
L |
1.6996073737924 |
L(r)(E,1)/r! |
Ω |
0.84980341503189 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117312db1 3666g1 |
Quadratic twists by: -4 8 |