Atkin-Lehner |
2+ 3+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68952c |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
538560 |
Modular degree for the optimal curve |
Δ |
-47370552512115456 = -1 · 28 · 33 · 136 · 175 |
Discriminant |
Eigenvalues |
2+ 3+ -3 0 1 13+ 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,86303,-3826811] |
[a1,a2,a3,a4,a6] |
Generators |
[45:382:1] |
Generators of the group modulo torsion |
j |
57530252288/38336139 |
j-invariant |
L |
3.9518391095887 |
L(r)(E,1)/r! |
Ω |
0.20367444131866 |
Real period |
R |
4.8506811698131 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000122 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
408c1 |
Quadratic twists by: 13 |