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	12768n	Isogeny class
Conductor	12768	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	30030336 = 29 · 32 · 73 · 19	Discriminant
Eigenvalues	2- 3+  2 7-  0 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-625632,190678680]	[a1,a2,a3,a4,a6]
Generators	[3706:1855:8]	Generators of the group modulo torsion
j	52894596367017490184/58653	j-invariant
L	4.5437988246743	L(r)(E,1)/r!
Ω	0.93034817941621	Real period
R	3.2559844620219	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	12768z2 25536do4 38304r4 89376cx4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12768n3

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 12768n3

-4	8	-3	-7
12768z2	25536do4	38304r4	89376cx4

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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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