Cremona's table of elliptic curves

2844 = 2² · 3² · 79

Field	Data	Notes
Atkin-Lehner	2- 3- 79+	Signs for the Atkin-Lehner involutions
Class	2844b	Isogeny class
Conductor	2844	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	-1965465648 = -1 · 24 · 39 · 792	Discriminant
Eigenvalues	2- 3- -2  0  2  2 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,2261]	[a1,a2,a3,a4,a6]
Generators	[-5:54:1]	Generators of the group modulo torsion
j	-35995648/168507	j-invariant
L	3.021965931185	L(r)(E,1)/r!
Ω	1.2824131477609	Real period
R	1.1782341503833	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	11376s1 45504n1 948a1 71100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2844b1

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	2	-8	0	6	-4	8	-2	-4	4	-12	4	-4	6	-4	-4	6	+	-6	-6	10

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Quadratic twists for elliptic curve 2844b1

-4	8	-3	5
11376s1	45504n1	948a1	71100e1

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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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