Cremona's table of elliptic curves

2838 = 2 · 3 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 43+	Signs for the Atkin-Lehner involutions
Class	2838d	Isogeny class
Conductor	2838	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	4359168 = 210 · 32 · 11 · 43	Discriminant
Eigenvalues	2- 3-  0 -4 11+  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-78,-252]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	52523718625/4359168	j-invariant
L	5.0562160811237	L(r)(E,1)/r!
Ω	1.614853283829	Real period
R	0.62621367919378	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	22704bb1 90816t1 8514c1 70950d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2838d1

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

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Quadratic twists for elliptic curve 2838d1

-4	8	-3	5	-11	-43
22704bb1	90816t1	8514c1	70950d1	31218h1	122034a1

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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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