Atkin-Lehner |
3- 5- 7+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615q |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
199680 |
Modular degree for the optimal curve |
Δ |
-72056798545095 = -1 · 38 · 5 · 7 · 13 · 176 |
Discriminant |
Eigenvalues |
-1 3- 5- 7+ 2 13+ 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-44132,-3580666] |
[a1,a2,a3,a4,a6] |
Generators |
[1016444:-27382077:1331] |
Generators of the group modulo torsion |
j |
-13039105118748409/98843345055 |
j-invariant |
L |
3.813023578046 |
L(r)(E,1)/r! |
Ω |
0.16462103791983 |
Real period |
R |
11.581215945283 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999986194 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205i1 |
Quadratic twists by: -3 |