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	2730w	Isogeny class
Conductor	2730	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-24584858584650 = -1 · 2 · 38 · 52 · 78 · 13	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-585,-238863]	[a1,a2,a3,a4,a6]
j	-22143063655441/24584858584650	j-invariant
L	2.4286434708265	L(r)(E,1)/r!
Ω	0.30358043385331	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21840ck5 87360bw5 8190k6 13650be6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730w6

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

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Quadratic twists for elliptic curve 2730w6

-4	8	-3	5	-7	13
21840ck5	87360bw5	8190k6	13650be6	19110co6	35490i5

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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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