Atkin-Lehner |
2+ 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
112112a |
Isogeny class |
Conductor |
112112 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
2775360 |
Modular degree for the optimal curve |
Δ |
-63664957584820592 = -1 · 24 · 78 · 11 · 137 |
Discriminant |
Eigenvalues |
2+ 3 4 7+ 11+ 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,20237,-12089035] |
[a1,a2,a3,a4,a6] |
Generators |
[2069950520726341860053559508350735662403954130677975983191109508420:24889953913584873944902316957485630678919674073644517204591054358355:8174743026230375908985376669365272869189704691947014686548628609] |
Generators of the group modulo torsion |
j |
9937057536/690233687 |
j-invariant |
L |
17.343448577227 |
L(r)(E,1)/r! |
Ω |
0.1665125403036 |
Real period |
R |
104.15701151159 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
56056m1 112112l1 |
Quadratic twists by: -4 -7 |