Atkin-Lehner |
5+ 7+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51205a |
Isogeny class |
Conductor |
51205 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
12960 |
Modular degree for the optimal curve |
Δ |
303594445 = 5 · 74 · 113 · 19 |
Discriminant |
Eigenvalues |
0 1 5+ 7+ 11- -4 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-261,1306] |
[a1,a2,a3,a4,a6] |
Generators |
[4:18:1] |
Generators of the group modulo torsion |
j |
822083584/126445 |
j-invariant |
L |
4.2988251040128 |
L(r)(E,1)/r! |
Ω |
1.6520099560531 |
Real period |
R |
2.6021786904372 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999564 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
51205p1 |
Quadratic twists by: -7 |