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	12768x	Isogeny class
Conductor	12768	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	84480	Modular degree for the optimal curve
Δ	5226887232 = 26 · 35 · 72 · 193	Discriminant
Eigenvalues	2- 3- -2 7+  2 -6  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-555574,159204920]	[a1,a2,a3,a4,a6]
Generators	[428:72:1]	Generators of the group modulo torsion
j	296326341756254404288/81670113	j-invariant
L	4.6815595574934	L(r)(E,1)/r!
Ω	0.80487667739329	Real period
R	1.1632985993967	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12768r1 25536bx1 38304i1 89376bw1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12768x1

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	+	2	-6	4	+	8	-2	-10	-4	-2	8	6	14	12	-2	10	0	2	-12	0	-18	-16

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Quadratic twists for elliptic curve 12768x1

-4	8	-3	-7
12768r1	25536bx1	38304i1	89376bw1

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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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