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	2838c	Isogeny class
Conductor	2838	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-13077504 = -1 · 210 · 33 · 11 · 43	Discriminant
Eigenvalues	2+ 3- -1 -3 11-  4  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-59,-250]	[a1,a2,a3,a4,a6]
Generators	[15:40:1]	Generators of the group modulo torsion
j	-22164361129/13077504	j-invariant
L	2.6382099724237	L(r)(E,1)/r!
Ω	0.8403118893739	Real period
R	0.52326007477798	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	22704v1 90816k1 8514g1 70950bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2838c1

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	-	4	3	-4	-6	2	3	-10	1	+	-2	0	14	-5	13	-1	-9	4	1	-5	-13

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Quadratic twists for elliptic curve 2838c1

-4	8	-3	5	-11	-43
22704v1	90816k1	8514g1	70950bj1	31218s1	122034h1

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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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