Atkin-Lehner |
2+ 5+ 17- 73- |
Signs for the Atkin-Lehner involutions |
Class |
12410b |
Isogeny class |
Conductor |
12410 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
99893788672000 = 217 · 53 · 174 · 73 |
Discriminant |
Eigenvalues |
2+ -1 5+ -3 -3 -4 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-264693,-52523987] |
[a1,a2,a3,a4,a6] |
Generators |
[-299:158:1] |
Generators of the group modulo torsion |
j |
2050943254369102052569/99893788672000 |
j-invariant |
L |
1.5536614695847 |
L(r)(E,1)/r! |
Ω |
0.2104820166877 |
Real period |
R |
1.8453612974096 |
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 |
99280q1 111690bz1 62050r1 |
Quadratic twists by: -4 -3 5 |