Atkin-Lehner |
2+ 3- 5- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
51480z |
Isogeny class |
Conductor |
51480 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-372086732160000 = -1 · 210 · 37 · 54 · 112 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 5- 4 11- 13- -4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,13173,-722954] |
[a1,a2,a3,a4,a6] |
Generators |
[87:1040:1] |
Generators of the group modulo torsion |
j |
338649393884/498444375 |
j-invariant |
L |
8.1322478996414 |
L(r)(E,1)/r! |
Ω |
0.28417487886886 |
Real period |
R |
1.192377256681 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000052 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
102960bk1 17160v1 |
Quadratic twists by: -4 -3 |