Atkin-Lehner |
2+ 7+ 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
47138a |
Isogeny class |
Conductor |
47138 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
229680 |
Modular degree for the optimal curve |
Δ |
-17315463438728 = -1 · 23 · 74 · 13 · 375 |
Discriminant |
Eigenvalues |
2+ 0 0 7+ -4 13+ 4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-292147,-60705891] |
[a1,a2,a3,a4,a6] |
Generators |
[494348520611787965:-5682723130320368107:725627513984381] |
Generators of the group modulo torsion |
j |
-1148515025417699625/7211771528 |
j-invariant |
L |
3.0507969918995 |
L(r)(E,1)/r! |
Ω |
0.10267600630335 |
Real period |
R |
29.71285212327 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47138d1 |
Quadratic twists by: -7 |