Atkin-Lehner |
3+ 5+ 29- 47- |
Signs for the Atkin-Lehner involutions |
Class |
61335a |
Isogeny class |
Conductor |
61335 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
444096 |
Modular degree for the optimal curve |
Δ |
-2462720044921875 = -1 · 39 · 59 · 29 · 472 |
Discriminant |
Eigenvalues |
2 3+ 5+ -4 3 -2 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-16983,-2535037] |
[a1,a2,a3,a4,a6] |
Generators |
[14606262:538252717:10648] |
Generators of the group modulo torsion |
j |
-27521724837888/125119140625 |
j-invariant |
L |
8.9710394709634 |
L(r)(E,1)/r! |
Ω |
0.1896570717384 |
Real period |
R |
11.825342694164 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000279 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61335b1 |
Quadratic twists by: -3 |