Cremona's table of elliptic curves

4046 = 2 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	4046a	Isogeny class
Conductor	4046	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	32368 = 24 · 7 · 172	Discriminant
Eigenvalues	2+  1  2 7+ -2  2 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15,18]	[a1,a2,a3,a4,a6]
Generators	[3:0:1]	Generators of the group modulo torsion
j	1171657/112	j-invariant
L	3.3502550912321	L(r)(E,1)/r!
Ω	3.5950066907651	Real period
R	0.46595950709053	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	32368ba1 129472g1 36414cj1 101150cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046a1

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	2	+	-2	2	+	-3	0	-3	5	-2	0	0	7	-7	3	-6	-14	-16	4	0	7	10	-18

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Quadratic twists for elliptic curve 4046a1

-4	8	-3	5	-7	17
32368ba1	129472g1	36414cj1	101150cj1	28322f1	4046g1

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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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