Atkin-Lehner |
2- 3+ 23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344o |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
570240 |
Modular degree for the optimal curve |
Δ |
20825299985891328 = 239 · 33 · 23 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 -5 -3 -4 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-70128,1722816] |
[a1,a2,a3,a4,a6] |
Generators |
[1640:65536:1] [2:1258:1] |
Generators of the group modulo torsion |
j |
9312028938816625/5084301754368 |
j-invariant |
L |
7.2468436549608 |
L(r)(E,1)/r! |
Ω |
0.33387455344072 |
Real period |
R |
5.4263222371106 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999968 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8418g1 |
Quadratic twists by: -4 |