Atkin-Lehner |
3+ 5+ 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
9735c |
Isogeny class |
Conductor |
9735 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
45283778525390625 = 310 · 510 · 113 · 59 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -4 11- 6 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-254761,-48529042] |
[a1,a2,a3,a4,a6] |
Generators |
[824:16962:1] |
Generators of the group modulo torsion |
j |
1828616581180443279889/45283778525390625 |
j-invariant |
L |
1.7053843294423 |
L(r)(E,1)/r! |
Ω |
0.21282466626818 |
Real period |
R |
2.6710317610982 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29205k1 48675s1 107085d1 |
Quadratic twists by: -3 5 -11 |