Atkin-Lehner |
2- 3+ 5+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030bb |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
384 |
Product of Tamagawa factors cp |
deg |
540672 |
Modular degree for the optimal curve |
Δ |
-338312296857600 = -1 · 216 · 33 · 52 · 133 · 592 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 -4 13- -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-75383,8034127] |
[a1,a2,a3,a4,a6] |
Generators |
[5601:-33494:27] [-197:3998:1] |
Generators of the group modulo torsion |
j |
-1754586557622582867/12530085068800 |
j-invariant |
L |
13.397978477908 |
L(r)(E,1)/r! |
Ω |
0.54339350243552 |
Real period |
R |
0.25683464227351 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999831 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69030d1 |
Quadratic twists by: -3 |