Atkin-Lehner |
2+ 3- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
30576u |
Isogeny class |
Conductor |
30576 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
-16356866512896 = -1 · 211 · 39 · 74 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -3 7+ -5 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-40392,3117204] |
[a1,a2,a3,a4,a6] |
Generators |
[324:4914:1] [114:-84:1] |
Generators of the group modulo torsion |
j |
-1482171386066/3326427 |
j-invariant |
L |
8.2672903709473 |
L(r)(E,1)/r! |
Ω |
0.69714540141496 |
Real period |
R |
0.054901735535231 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15288c1 122304et1 91728q1 30576o1 |
Quadratic twists by: -4 8 -3 -7 |