Atkin-Lehner |
2- 3+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
23712m |
Isogeny class |
Conductor |
23712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
214272 |
Modular degree for the optimal curve |
Δ |
-7188783353856 = -1 · 212 · 39 · 13 · 193 |
Discriminant |
Eigenvalues |
2- 3+ 1 -3 4 13- 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1530705,729439713] |
[a1,a2,a3,a4,a6] |
Generators |
[713:76:1] |
Generators of the group modulo torsion |
j |
-96836380962843416896/1755074061 |
j-invariant |
L |
4.7986058543805 |
L(r)(E,1)/r! |
Ω |
0.53430253857304 |
Real period |
R |
2.2452662620676 |
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 |
23712j1 47424bi1 71136k1 |
Quadratic twists by: -4 8 -3 |