Atkin-Lehner |
2+ 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312bd |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
96768 |
Modular degree for the optimal curve |
Δ |
-1167409262592 = -1 · 212 · 37 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 -6 -3 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,2407,-24441] |
[a1,a2,a3,a4,a6] |
Generators |
[25:-228:1] [13:96:1] |
Generators of the group modulo torsion |
j |
2888000/2187 |
j-invariant |
L |
10.941541404604 |
L(r)(E,1)/r! |
Ω |
0.48438603673134 |
Real period |
R |
0.53782080991317 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312b1 34656b1 69312l1 |
Quadratic twists by: -4 8 -19 |