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	2842d	Isogeny class
Conductor	2842	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-2249563705424 = -1 · 24 · 78 · 293	Discriminant
Eigenvalues	2+ -1  3 7- -3  1  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-711,-72827]	[a1,a2,a3,a4,a6]
Generators	[202:2741:1]	Generators of the group modulo torsion
j	-338608873/19120976	j-invariant
L	2.4054377820102	L(r)(E,1)/r!
Ω	0.36054085440889	Real period
R	0.55597901333399	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22736bi1 90944t1 25578bl1 71050ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2842d1

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	-	-3	1	0	4	-6	-	-5	2	0	-7	3	-9	-12	10	2	-12	-8	5	-12	-6	-8

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Quadratic twists for elliptic curve 2842d1

-4	8	-3	5	-7	29
22736bi1	90944t1	25578bl1	71050ca1	406b1	82418m1

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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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