Atkin-Lehner |
2+ 3- 7- 79- |
Signs for the Atkin-Lehner involutions |
Class |
69678p |
Isogeny class |
Conductor |
69678 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
528384 |
Modular degree for the optimal curve |
Δ |
-57527869206528 = -1 · 212 · 38 · 73 · 792 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- -4 -4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-106164,13345744] |
[a1,a2,a3,a4,a6] |
Generators |
[177:188:1] [142:27019:8] |
Generators of the group modulo torsion |
j |
-529219922424103/230068224 |
j-invariant |
L |
5.3652673115087 |
L(r)(E,1)/r! |
Ω |
0.61662019156919 |
Real period |
R |
2.1752723089684 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000044 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23226u1 69678o1 |
Quadratic twists by: -3 -7 |