Atkin-Lehner |
2- 3+ 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
77376bd |
Isogeny class |
Conductor |
77376 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
668160 |
Modular degree for the optimal curve |
Δ |
-4349436793847808 = -1 · 217 · 3 · 135 · 313 |
Discriminant |
Eigenvalues |
2- 3+ -4 -1 0 13+ 5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-190945,-32207999] |
[a1,a2,a3,a4,a6] |
Generators |
[509:1488:1] |
Generators of the group modulo torsion |
j |
-5874094542556658/33183569289 |
j-invariant |
L |
3.3417102910955 |
L(r)(E,1)/r! |
Ω |
0.11415517838482 |
Real period |
R |
2.4394500667273 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002269 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77376p1 19344i1 |
Quadratic twists by: -4 8 |