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	2046g	Isogeny class
Conductor	2046	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-17163091968 = -1 · 224 · 3 · 11 · 31	Discriminant
Eigenvalues	2- 3+ -2  0 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1344,19425]	[a1,a2,a3,a4,a6]
j	-268498407453697/17163091968	j-invariant
L	1.8198641983391	L(r)(E,1)/r!
Ω	1.2132427988927	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16368ba1 65472y1 6138g1 51150r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046g1

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	4	0	6	+	-2	10	4	8	6	-4	14	4	0	-6	8	12	10	2

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Quadratic twists for elliptic curve 2046g1

-4	8	-3	5	-7	-11	-31
16368ba1	65472y1	6138g1	51150r1	100254cp1	22506f1	63426bi1

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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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