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	12768z	Isogeny class
Conductor	12768	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	220171162176 = 26 · 34 · 76 · 192	Discriminant
Eigenvalues	2- 3-  2 7+  0 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-39102,-2989080]	[a1,a2,a3,a4,a6]
j	103312235477340352/3440174409	j-invariant
L	2.7160623848927	L(r)(E,1)/r!
Ω	0.33950779811159	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12768n1 25536bs2 38304n1 89376bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12768z1

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	-2	-6	-	0	-2	0	6	6	0	-8	6	4	2	4	12	2	-4	12	14	-10

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Quadratic twists for elliptic curve 12768z1

-4	8	-3	-7
12768n1	25536bs2	38304n1	89376bm1

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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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