Atkin-Lehner |
3+ 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
27075g |
Isogeny class |
Conductor |
27075 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
-11026378359375 = -1 · 3 · 57 · 196 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 0 -4 -2 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-188,-159844] |
[a1,a2,a3,a4,a6] |
Generators |
[80:547:1] [131:1378:1] |
Generators of the group modulo torsion |
j |
-1/15 |
j-invariant |
L |
4.4922415976153 |
L(r)(E,1)/r! |
Ω |
0.3275419929183 |
Real period |
R |
6.857504831048 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999969 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81225z1 5415k1 75b1 |
Quadratic twists by: -3 5 -19 |