Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828i |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1520640 |
Modular degree for the optimal curve |
Δ |
652582464473808 = 24 · 32 · 113 · 237 |
Discriminant |
Eigenvalues |
2- 3+ 4 0 11+ -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5398621,4829856658] |
[a1,a2,a3,a4,a6] |
Generators |
[1382896242:24434510:1030301] |
Generators of the group modulo torsion |
j |
7346581704933376/275517 |
j-invariant |
L |
6.8698438830813 |
L(r)(E,1)/r! |
Ω |
0.37842494067529 |
Real period |
R |
9.0768910080639 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000868 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3036e1 |
Quadratic twists by: -23 |