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	2730p	Isogeny class
Conductor	2730	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1817088000000000 = 218 · 3 · 59 · 7 · 132	Discriminant
Eigenvalues	2+ 3- 5+ 7- -6 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-852274,-302906428]	[a1,a2,a3,a4,a6]
j	68463752473882049153689/1817088000000000	j-invariant
L	1.4141582348171	L(r)(E,1)/r!
Ω	0.15712869275745	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21840be5 87360bj5 8190bz5 13650bu5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730p5

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

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Quadratic twists for elliptic curve 2730p5

-4	8	-3	5	-7	13
21840be5	87360bj5	8190bz5	13650bu5	19110m5	35490dp5

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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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