Atkin-Lehner |
3+ 5+ 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
45045f |
Isogeny class |
Conductor |
45045 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
38016 |
Modular degree for the optimal curve |
Δ |
-50174679555 = -1 · 33 · 5 · 7 · 11 · 136 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7- 11+ 13- -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-3708,87573] |
[a1,a2,a3,a4,a6] |
Generators |
[34:2141:8] |
Generators of the group modulo torsion |
j |
-208823381655552/1858321465 |
j-invariant |
L |
3.997731444414 |
L(r)(E,1)/r! |
Ω |
1.1324358986706 |
Real period |
R |
2.6476541293266 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999916 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
45045l2 |
Quadratic twists by: -3 |