Atkin-Lehner |
2+ 3+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68952b |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
602112 |
Modular degree for the optimal curve |
Δ |
1150219471684608 = 210 · 34 · 138 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 -6 13+ 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-71712,-7185348] |
[a1,a2,a3,a4,a6] |
Generators |
[2466:121680:1] |
Generators of the group modulo torsion |
j |
8251733668/232713 |
j-invariant |
L |
3.7027578598019 |
L(r)(E,1)/r! |
Ω |
0.29224658463635 |
Real period |
R |
3.1674945532106 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991405 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5304g1 |
Quadratic twists by: 13 |