Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825x |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
85536 |
Modular degree for the optimal curve |
Δ |
-8704314675 = -1 · 39 · 52 · 72 · 192 |
Discriminant |
Eigenvalues |
2 3+ 5+ 7- -6 2 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1388,20873] |
[a1,a2,a3,a4,a6] |
Generators |
[314:1269:8] |
Generators of the group modulo torsion |
j |
-241584394240/7105563 |
j-invariant |
L |
9.1808271348555 |
L(r)(E,1)/r! |
Ω |
1.2992473996769 |
Real period |
R |
3.5331327723536 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000051 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69825ck1 69825bh1 |
Quadratic twists by: 5 -7 |