Atkin-Lehner |
3- 5+ 7- 23- |
Signs for the Atkin-Lehner involutions |
Class |
84525ct |
Isogeny class |
Conductor |
84525 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
1152000 |
Modular degree for the optimal curve |
Δ |
-38044868538796875 = -1 · 35 · 56 · 77 · 233 |
Discriminant |
Eigenvalues |
-2 3- 5+ 7- -5 -2 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-118008,18168644] |
[a1,a2,a3,a4,a6] |
Generators |
[177:-1691:1] [-192:5812:1] |
Generators of the group modulo torsion |
j |
-98867482624/20696067 |
j-invariant |
L |
6.8308005801445 |
L(r)(E,1)/r! |
Ω |
0.34905429555055 |
Real period |
R |
0.16307874990263 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000236 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3381c1 12075m1 |
Quadratic twists by: 5 -7 |