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	2842b	Isogeny class
Conductor	2842	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	246721276548717824 = 28 · 716 · 29	Discriminant
Eigenvalues	2+ -2 -2 7-  4  2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1922982,1025947640]	[a1,a2,a3,a4,a6]
j	6684374974140996553/2097096248576	j-invariant
L	0.61110565091475	L(r)(E,1)/r!
Ω	0.30555282545737	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22736bc2 90944cc2 25578bv2 71050bu2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2842b2

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	-	4	2	4	-2	0	+	2	2	-8	-8	-6	6	4	-4	-4	8	12	-12	0	-4	-4

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Quadratic twists for elliptic curve 2842b2

-4	8	-3	5	-7	29
22736bc2	90944cc2	25578bv2	71050bu2	406d2	82418o2

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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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