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	2730o	Isogeny class
Conductor	2730	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	7751016000 = 26 · 32 · 53 · 72 · 133	Discriminant
Eigenvalues	2+ 3- 5+ 7-  6 13-  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-51474,-4499228]	[a1,a2,a3,a4,a6]
j	15082569606665230489/7751016000	j-invariant
L	1.9017562385998	L(r)(E,1)/r!
Ω	0.31695937309996	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21840bf3 87360bk3 8190ca3 13650bs3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730o3

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

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Quadratic twists for elliptic curve 2730o3

-4	8	-3	5	-7	13
21840bf3	87360bk3	8190ca3	13650bs3	19110l3	35490dq3

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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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