Atkin-Lehner |
2- 3- 5+ 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
84420m |
Isogeny class |
Conductor |
84420 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
542802027600 = 24 · 310 · 52 · 73 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- -2 -6 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-68808,6947057] |
[a1,a2,a3,a4,a6] |
Generators |
[166:-315:1] [-212:3465:1] |
Generators of the group modulo torsion |
j |
3088822876635136/46536525 |
j-invariant |
L |
10.23859499365 |
L(r)(E,1)/r! |
Ω |
0.84497434429445 |
Real period |
R |
0.67316935339911 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998778 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28140f1 |
Quadratic twists by: -3 |