Atkin-Lehner |
2+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
59488m |
Isogeny class |
Conductor |
59488 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
554112 |
Modular degree for the optimal curve |
Δ |
-7226669396717056 = -1 · 29 · 113 · 139 |
Discriminant |
Eigenvalues |
2+ 0 1 3 11- 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2265107,1312149462] |
[a1,a2,a3,a4,a6] |
Generators |
[-1183:48334:1] |
Generators of the group modulo torsion |
j |
-236717162856/1331 |
j-invariant |
L |
6.8749100729399 |
L(r)(E,1)/r! |
Ω |
0.37206585262096 |
Real period |
R |
1.5398058400038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000231 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
59488i1 118976cr1 59488q1 |
Quadratic twists by: -4 8 13 |