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	2730v	Isogeny class
Conductor	2730	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	71987251059360000 = 28 · 38 · 54 · 74 · 134	Discriminant
Eigenvalues	2- 3+ 5- 7+  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-350720,78749345]	[a1,a2,a3,a4,a6]
j	4770955732122964500481/71987251059360000	j-invariant
L	2.7727274484007	L(r)(E,1)/r!
Ω	0.34659093105009	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	21840cl3 87360bx3 8190l4 13650bd3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730v3

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

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Quadratic twists for elliptic curve 2730v3

-4	8	-3	5	-7	13
21840cl3	87360bx3	8190l4	13650bd3	19110cm4	35490k3

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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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