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	4140i	Isogeny class
Conductor	4140	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-21461760 = -1 · 28 · 36 · 5 · 23	Discriminant
Eigenvalues	2- 3- 5- -1 -6  6 -7  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-72,324]	[a1,a2,a3,a4,a6]
Generators	[0:18:1]	Generators of the group modulo torsion
j	-221184/115	j-invariant
L	3.6856335636047	L(r)(E,1)/r!
Ω	2.0015883236659	Real period
R	0.30689240806308	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	16560bu1 66240bx1 460a1 20700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4140i1

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	-6	6	-7	2	-	5	1	-5	7	8	-8	-3	-13	-8	-9	-7	-2	-12	5	12	2

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Quadratic twists for elliptic curve 4140i1

-4	8	-3	5	-23
16560bu1	66240bx1	460a1	20700h1	95220j1

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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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