Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
67032bb |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
4423680 |
Modular degree for the optimal curve |
Δ |
319453080494505552 = 24 · 312 · 711 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 0 2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-46937982,-123775509935] |
[a1,a2,a3,a4,a6] |
Generators |
[3615276:1321143047:27] |
Generators of the group modulo torsion |
j |
8334147900493981696/232793757 |
j-invariant |
L |
4.2942355410623 |
L(r)(E,1)/r! |
Ω |
0.057679096900989 |
Real period |
R |
9.3063080302712 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993353 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22344bg1 9576k1 |
Quadratic twists by: -3 -7 |