Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744t |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
-60379349184 = -1 · 26 · 36 · 76 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11- 2 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,278,-11780] |
[a1,a2,a3,a4,a6] |
Generators |
[1020:6110:27] |
Generators of the group modulo torsion |
j |
314432/8019 |
j-invariant |
L |
6.2644991937782 |
L(r)(E,1)/r! |
Ω |
0.53695128403071 |
Real period |
R |
5.8333962317198 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000023 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744bm1 103488hv2 1056f1 |
Quadratic twists by: -4 8 -7 |