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	16	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	4542720 = 28 · 3 · 5 · 7 · 132	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-375,2637]	[a1,a2,a3,a4,a6]
j	5832972054001/4542720	j-invariant
L	2.4286434708265	L(r)(E,1)/r!
Ω	2.4286434708265	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840ck1 87360bw1 8190k1 13650be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730w1

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 2730w1

-4	8	-3	5	-7	13
21840ck1	87360bw1	8190k1	13650be1	19110co1	35490i1

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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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