Atkin-Lehner |
2+ 3- 7+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
51282h |
Isogeny class |
Conductor |
51282 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
-2369262926724857856 = -1 · 220 · 311 · 7 · 113 · 372 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11+ 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,310842,32091700] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:5126:1] [233:10706:1] |
Generators of the group modulo torsion |
j |
4556322767940900767/3250017732132864 |
j-invariant |
L |
6.4398437439848 |
L(r)(E,1)/r! |
Ω |
0.16403200075797 |
Real period |
R |
19.629839647833 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17094s1 |
Quadratic twists by: -3 |