Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312df |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
409600 |
Modular degree for the optimal curve |
Δ |
-4837498213810176 = -1 · 214 · 316 · 193 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 -3 0 -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-16517,-3450141] |
[a1,a2,a3,a4,a6] |
Generators |
[310:4617:1] |
Generators of the group modulo torsion |
j |
-4434684928/43046721 |
j-invariant |
L |
4.6224527007629 |
L(r)(E,1)/r! |
Ω |
0.18354557434036 |
Real period |
R |
0.78700697318379 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997196 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312g1 17328d1 69312cj1 |
Quadratic twists by: -4 8 -19 |