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	4046c	Isogeny class
Conductor	4046	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3161078435904032 = 25 · 72 · 1710	Discriminant
Eigenvalues	2+ -2 -4 7+  4 -4 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-37143,-526438]	[a1,a2,a3,a4,a6]
Generators	[-44:1033:1]	Generators of the group modulo torsion
j	234770924809/130960928	j-invariant
L	1.1135791218968	L(r)(E,1)/r!
Ω	0.36912503983033	Real period
R	1.5084036596496	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	32368bc2 129472j2 36414cp2 101150ck2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046c2

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

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Quadratic twists for elliptic curve 4046c2

-4	8	-3	5	-7	17
32368bc2	129472j2	36414cp2	101150ck2	28322g2	238e2

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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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