Atkin-Lehner |
2+ 3- 37- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
31302f |
Isogeny class |
Conductor |
31302 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5376 |
Modular degree for the optimal curve |
Δ |
-22819158 = -1 · 2 · 38 · 37 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 0 1 4 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-27,243] |
[a1,a2,a3,a4,a6] |
Generators |
[3:12:1] |
Generators of the group modulo torsion |
j |
-3048625/31302 |
j-invariant |
L |
4.2230481095379 |
L(r)(E,1)/r! |
Ω |
1.8239983630814 |
Real period |
R |
1.1576348408569 |
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 |
10434j1 |
Quadratic twists by: -3 |