Atkin-Lehner |
2+ 3+ 11- 53- |
Signs for the Atkin-Lehner involutions |
Class |
27984b |
Isogeny class |
Conductor |
27984 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
296960 |
Modular degree for the optimal curve |
Δ |
-311584053691723824 = -1 · 24 · 316 · 115 · 532 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 11- -2 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-62227,-27492110] |
[a1,a2,a3,a4,a6] |
Generators |
[5610:132235:8] |
Generators of the group modulo torsion |
j |
-1665510213736081408/19474003355732739 |
j-invariant |
L |
4.0536988115537 |
L(r)(E,1)/r! |
Ω |
0.1303529830643 |
Real period |
R |
6.2195719902384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13992b1 111936h1 83952b1 |
Quadratic twists by: -4 8 -3 |