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	4046d	Isogeny class
Conductor	4046	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	149669632 = 28 · 7 · 174	Discriminant
Eigenvalues	2+ -3 -2 7+ -2 -6 17-  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-343,2461]	[a1,a2,a3,a4,a6]
Generators	[-21:19:1] [-2:57:1]	Generators of the group modulo torsion
j	53520777/1792	j-invariant
L	2.0769632506993	L(r)(E,1)/r!
Ω	1.8183633717145	Real period
R	0.19036928876144	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368bk1 129472v1 36414cq1 101150cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046d1

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
+	-3	-2	+	-2	-6	-	7	-8	-9	5	2	0	-8	-7	-3	1	-2	-10	-8	-4	-16	-3	-6	10

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Quadratic twists for elliptic curve 4046d1

-4	8	-3	5	-7	17
32368bk1	129472v1	36414cq1	101150cq1	28322m1	4046f1

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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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