Atkin-Lehner |
2+ 3- 5- 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
51240j |
Isogeny class |
Conductor |
51240 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
5967360 |
Modular degree for the optimal curve |
Δ |
8680802054400 = 28 · 33 · 52 · 77 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ -4 4 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-452125100,3700141666848] |
[a1,a2,a3,a4,a6] |
Generators |
[105759708280:-82796136:8615125] |
Generators of the group modulo torsion |
j |
39926349238603024419142334416/33909383025 |
j-invariant |
L |
7.5179739060974 |
L(r)(E,1)/r! |
Ω |
0.21682105713041 |
Real period |
R |
11.557877888684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000095 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
102480h1 |
Quadratic twists by: -4 |