Atkin-Lehner |
2+ 5+ 23- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
61640b |
Isogeny class |
Conductor |
61640 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
298752 |
Modular degree for the optimal curve |
Δ |
-101564462725120 = -1 · 211 · 5 · 236 · 67 |
Discriminant |
Eigenvalues |
2+ -2 5+ -5 -1 -6 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-43976,-3597200] |
[a1,a2,a3,a4,a6] |
Generators |
[299:3174:1] [391:6256:1] |
Generators of the group modulo torsion |
j |
-4592517367756178/49592022815 |
j-invariant |
L |
5.1399132211704 |
L(r)(E,1)/r! |
Ω |
0.16473479004077 |
Real period |
R |
5.2001899739297 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
123280b1 |
Quadratic twists by: -4 |