Cremona's table of elliptic curves

2046 = 2 · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 31-	Signs for the Atkin-Lehner involutions
Class	2046j	Isogeny class
Conductor	2046	Conductor
∏ cp	672	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	183328572506112 = 216 · 37 · 113 · 312	Discriminant
Eigenvalues	2- 3- -2 -2 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-63289,6088313]	[a1,a2,a3,a4,a6]
Generators	[26:2099:1]	Generators of the group modulo torsion
j	28035534600833657617/183328572506112	j-invariant
L	4.3590633944629	L(r)(E,1)/r!
Ω	0.57187578479353	Real period
R	0.045371401638889	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	16368n1 65472d1 6138f1 51150j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046j1

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	-6	-2	4	-6	-	-2	-10	0	2	-4	10	4	8	-6	0	-12	-4	16	-2

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Quadratic twists for elliptic curve 2046j1

-4	8	-3	5	-7	-11	-31
16368n1	65472d1	6138f1	51150j1	100254br1	22506r1	63426v1

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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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