Cremona's table of elliptic curves

12768 = 2⁵ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	12768m	Isogeny class
Conductor	12768	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	354988532523921408 = 212 · 36 · 7 · 198	Discriminant
Eigenvalues	2- 3+  2 7+  0 -6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-200977,-19449983]	[a1,a2,a3,a4,a6]
Generators	[-6009:101764:27]	Generators of the group modulo torsion
j	219182059128501568/86667122198223	j-invariant
L	4.2157917017082	L(r)(E,1)/r!
Ω	0.23327223755796	Real period
R	4.5181026960621	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12768bc2 25536cu1 38304o3 89376co3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12768m3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	2	+	0	-6	2	-	0	6	0	6	2	-8	-8	-10	4	10	8	0	10	0	4	-6	2

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Quadratic twists for elliptic curve 12768m3

-4	8	-3	-7
12768bc2	25536cu1	38304o3	89376co3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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