Atkin-Lehner |
2+ 3- 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
30690o |
Isogeny class |
Conductor |
30690 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-15412518000 = -1 · 24 · 36 · 53 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 11+ -2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-114,6020] |
[a1,a2,a3,a4,a6] |
Generators |
[11:-83:1] [-11:82:1] |
Generators of the group modulo torsion |
j |
-225866529/21142000 |
j-invariant |
L |
5.9954392716908 |
L(r)(E,1)/r! |
Ω |
1.0225718735653 |
Real period |
R |
0.9771830268823 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3410c1 |
Quadratic twists by: -3 |