Cremona's table of elliptic curves

4060 = 2² · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	4060a	Isogeny class
Conductor	4060	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	568400 = 24 · 52 · 72 · 29	Discriminant
Eigenvalues	2- -2 5+ 7+ -2 -6 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,4]	[a1,a2,a3,a4,a6]
Generators	[-5:3:1] [-3:7:1]	Generators of the group modulo torsion
j	67108864/35525	j-invariant
L	3.2101607415887	L(r)(E,1)/r!
Ω	2.5522134438917	Real period
R	0.41926492593755	Regulator
r	2	Rank of the group of rational points
S	0.99999999999955	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16240o1 64960o1 36540n1 20300h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4060a1

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

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Quadratic twists for elliptic curve 4060a1

-4	8	-3	5	-7	29
16240o1	64960o1	36540n1	20300h1	28420f1	117740b1

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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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