Cremona's table of elliptic curves

4140 = 2² · 3² · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23-	Signs for the Atkin-Lehner involutions
Class	4140g	Isogeny class
Conductor	4140	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-4442584320 = -1 · 28 · 38 · 5 · 232	Discriminant
Eigenvalues	2- 3- 5-  0  0 -6 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,33,3206]	[a1,a2,a3,a4,a6]
Generators	[-5:54:1]	Generators of the group modulo torsion
j	21296/23805	j-invariant
L	3.8021737008639	L(r)(E,1)/r!
Ω	1.0783831396597	Real period
R	0.58763494485886	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	16560bs2 66240br2 1380a2 20700e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4140g2

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
-	-	-	0	0	-6	-2	6	-	-6	-4	4	-6	4	4	-6	-14	6	-4	2	10	-14	-4	-18	12

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Quadratic twists for elliptic curve 4140g2

-4	8	-3	5	-23
16560bs2	66240br2	1380a2	20700e2	95220g2

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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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