Atkin-Lehner |
2+ 3- 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
127680ca |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
233472 |
Modular degree for the optimal curve |
Δ |
-985226760000 = -1 · 26 · 33 · 54 · 7 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -4 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2756,72450] |
[a1,a2,a3,a4,a6] |
Generators |
[1:264:1] [37:150:1] |
Generators of the group modulo torsion |
j |
-36185864262976/15394168125 |
j-invariant |
L |
12.615014497839 |
L(r)(E,1)/r! |
Ω |
0.82360982323414 |
Real period |
R |
5.1055787772547 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999961245 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680r1 63840bm2 |
Quadratic twists by: -4 8 |