Atkin-Lehner |
3+ 5- 37- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
33855a |
Isogeny class |
Conductor |
33855 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-2586885433425 = -1 · 32 · 52 · 373 · 613 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 5 4 -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-185,77312] |
[a1,a2,a3,a4,a6] |
Generators |
[12:-284:1] |
Generators of the group modulo torsion |
j |
-700463661841/2586885433425 |
j-invariant |
L |
3.6179595365544 |
L(r)(E,1)/r! |
Ω |
0.65112236622324 |
Real period |
R |
0.46304142460198 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
101565e1 |
Quadratic twists by: -3 |