Atkin-Lehner |
2+ 7+ 17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
12614b |
Isogeny class |
Conductor |
12614 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55552 |
Modular degree for the optimal curve |
Δ |
-15384039243776 = -1 · 214 · 7 · 17 · 534 |
Discriminant |
Eigenvalues |
2+ 0 -2 7+ 2 -4 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-119848,-15940800] |
[a1,a2,a3,a4,a6] |
Generators |
[12761916344:-575049264661:6229504] |
Generators of the group modulo torsion |
j |
-190378597673833931097/15384039243776 |
j-invariant |
L |
2.3282685634571 |
L(r)(E,1)/r! |
Ω |
0.12829495709632 |
Real period |
R |
18.147779274824 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
100912r1 113526y1 88298l1 |
Quadratic twists by: -4 -3 -7 |