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	192	Product of Tamagawa factors cp
Δ	1073217600 = 26 · 34 · 52 · 72 · 132	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-256,-64]	[a1,a2,a3,a4,a6]
Generators	[-10:44:1]	Generators of the group modulo torsion
j	1855878893569/1073217600	j-invariant
L	4.9748694168706	L(r)(E,1)/r!
Ω	1.3063881278131	Real period
R	0.31734248236002	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840bg2 87360y2 8190p2 13650l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730y2

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 2730y2

-4	8	-3	5	-7	13
21840bg2	87360y2	8190p2	13650l2	19110cg2	35490bv2

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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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