Atkin-Lehner |
2+ 3+ 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
77376i |
Isogeny class |
Conductor |
77376 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-3910892544 = -1 · 210 · 36 · 132 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -3 0 13- -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,279,-2511] |
[a1,a2,a3,a4,a6] |
Generators |
[8:13:1] [72:621:1] |
Generators of the group modulo torsion |
j |
2337108224/3819231 |
j-invariant |
L |
8.1479615677282 |
L(r)(E,1)/r! |
Ω |
0.73434657529602 |
Real period |
R |
2.7738815165152 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77376bs1 4836d1 |
Quadratic twists by: -4 8 |