Atkin-Lehner |
2+ 5- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12350h |
Isogeny class |
Conductor |
12350 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
295680 |
Modular degree for the optimal curve |
Δ |
-141576341481250000 = -1 · 24 · 58 · 137 · 192 |
Discriminant |
Eigenvalues |
2+ 2 5- 5 3 13+ 7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-165575,31557125] |
[a1,a2,a3,a4,a6] |
j |
-1285144810759705/362435434192 |
j-invariant |
L |
3.7214353852627 |
L(r)(E,1)/r! |
Ω |
0.31011961543856 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98800ct1 111150ez1 12350r1 |
Quadratic twists by: -4 -3 5 |