Atkin-Lehner |
2+ 5- 11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
31240d |
Isogeny class |
Conductor |
31240 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
122112 |
Modular degree for the optimal curve |
Δ |
-519755500000000 = -1 · 28 · 59 · 114 · 71 |
Discriminant |
Eigenvalues |
2+ -2 5- -1 11- -5 -6 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11505,1191475] |
[a1,a2,a3,a4,a6] |
Generators |
[-135:550:1] [-85:1250:1] |
Generators of the group modulo torsion |
j |
-657932536001536/2030294921875 |
j-invariant |
L |
6.2558090384358 |
L(r)(E,1)/r! |
Ω |
0.45835126780713 |
Real period |
R |
0.094781276662138 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
62480f1 |
Quadratic twists by: -4 |