Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	2730y	Isogeny class
Conductor	2730	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	8191539720 = 23 · 38 · 5 · 74 · 13	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2856,-58824]	[a1,a2,a3,a4,a6]
Generators	[-30:24:1]	Generators of the group modulo torsion
j	2576367579235969/8191539720	j-invariant
L	4.9748694168706	L(r)(E,1)/r!
Ω	0.65319406390657	Real period
R	0.63468496472004	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	21840bg4 87360y4 8190p4 13650l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730y3

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

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Quadratic twists for elliptic curve 2730y3

-4	8	-3	5	-7	13
21840bg4	87360y4	8190p4	13650l3	19110cg4	35490bv4

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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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