Atkin-Lehner |
2+ 3+ 17- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
60384j |
Isogeny class |
Conductor |
60384 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
58368 |
Modular degree for the optimal curve |
Δ |
-60310573056 = -1 · 212 · 34 · 173 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -3 -3 -4 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1377,23409] |
[a1,a2,a3,a4,a6] |
Generators |
[153:1836:1] [17:-68:1] |
Generators of the group modulo torsion |
j |
-70547387968/14724261 |
j-invariant |
L |
6.0510752595168 |
L(r)(E,1)/r! |
Ω |
1.06231824047 |
Real period |
R |
0.23733766983166 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000015 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60384s1 120768dw1 |
Quadratic twists by: -4 8 |