Atkin-Lehner |
2+ 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312c |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-9102606336 = -1 · 214 · 34 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ 1 1 -1 4 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-405,-5427] |
[a1,a2,a3,a4,a6] |
Generators |
[522:3933:8] |
Generators of the group modulo torsion |
j |
-65536/81 |
j-invariant |
L |
6.4504491655808 |
L(r)(E,1)/r! |
Ω |
0.50819966791989 |
Real period |
R |
3.1731864328025 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999818 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312cz1 4332b1 69312be1 |
Quadratic twists by: -4 8 -19 |