Atkin-Lehner |
2+ 29+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
68672d |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
153600 |
Modular degree for the optimal curve |
Δ |
-131791241412608 = -1 · 216 · 29 · 375 |
Discriminant |
Eigenvalues |
2+ 1 0 0 -5 4 -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,7007,506431] |
[a1,a2,a3,a4,a6] |
Generators |
[-21:592:1] [8955:847504:1] |
Generators of the group modulo torsion |
j |
580467825500/2010974753 |
j-invariant |
L |
11.69503084319 |
L(r)(E,1)/r! |
Ω |
0.41455090441357 |
Real period |
R |
1.4105663163058 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999941 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672u1 8584c1 |
Quadratic twists by: -4 8 |