Cremona's table of elliptic curves

2842 = 2 · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29-	Signs for the Atkin-Lehner involutions
Class	2842f	Isogeny class
Conductor	2842	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-42797882624 = -1 · 28 · 78 · 29	Discriminant
Eigenvalues	2-  1  3 7- -1  1  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4999,-136823]	[a1,a2,a3,a4,a6]
j	-117433042273/363776	j-invariant
L	4.5413789558622	L(r)(E,1)/r!
Ω	0.28383618474139	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22736bl1 90944z1 25578q1 71050v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2842f1

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
-	1	3	-	-1	1	4	4	-2	-	1	6	0	3	9	3	0	-6	2	-8	0	-13	0	14	-16

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Quadratic twists for elliptic curve 2842f1

-4	8	-3	5	-7	29
22736bl1	90944z1	25578q1	71050v1	406c1	82418b1

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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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