Atkin-Lehner |
2+ 3- 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
23688h |
Isogeny class |
Conductor |
23688 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
112640 |
Modular degree for the optimal curve |
Δ |
767955336465744 = 24 · 311 · 78 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -4 -2 6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-41466,2963945] |
[a1,a2,a3,a4,a6] |
Generators |
[208:1827:1] |
Generators of the group modulo torsion |
j |
676009238591488/65839792221 |
j-invariant |
L |
4.4069333958981 |
L(r)(E,1)/r! |
Ω |
0.49076120478342 |
Real period |
R |
2.2449479262745 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
47376n1 7896j1 |
Quadratic twists by: -4 -3 |