Cremona's table of elliptic curves

28392 = 2³ · 3 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	28392q	Isogeny class
Conductor	28392	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	18387096998280192 = 210 · 312 · 7 · 136	Discriminant
Eigenvalues	2- 3+ -2 7+  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-66304,-766052]	[a1,a2,a3,a4,a6]
Generators	[-226:1620:1] [-82:2028:1]	Generators of the group modulo torsion
j	6522128932/3720087	j-invariant
L	6.3234423097626	L(r)(E,1)/r!
Ω	0.32193541662486	Real period
R	9.8209795866155	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	56784v3 85176o3 168b3	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 28392q3

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

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Quadratic twists for elliptic curve 28392q3

-4	-3	13
56784v3	85176o3	168b3

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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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