Atkin-Lehner |
5+ 7- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
51205i |
Isogeny class |
Conductor |
51205 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
645120 |
Modular degree for the optimal curve |
Δ |
-992841650753999585 = -1 · 5 · 711 · 114 · 193 |
Discriminant |
Eigenvalues |
-1 -1 5+ 7- 11+ -4 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-395676,-107288882] |
[a1,a2,a3,a4,a6] |
Generators |
[1574:-57113:1] |
Generators of the group modulo torsion |
j |
-58231056078442801/8439014787665 |
j-invariant |
L |
1.4352509527414 |
L(r)(E,1)/r! |
Ω |
0.094419905733459 |
Real period |
R |
1.2667270225655 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000094 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7315e1 |
Quadratic twists by: -7 |