Atkin-Lehner |
3- 7- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
30723x |
Isogeny class |
Conductor |
30723 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-9124731 = -1 · 34 · 72 · 112 · 19 |
Discriminant |
Eigenvalues |
0 3- -3 7- 11+ -6 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,33,137] |
[a1,a2,a3,a4,a6] |
Generators |
[3:-17:1] |
Generators of the group modulo torsion |
j |
78675968/186219 |
j-invariant |
L |
3.0648928828255 |
L(r)(E,1)/r! |
Ω |
1.6095220084877 |
Real period |
R |
0.23802818994265 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
92169bd1 30723b1 |
Quadratic twists by: -3 -7 |