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	2730x	Isogeny class
Conductor	2730	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-187320324116835000 = -1 · 23 · 38 · 54 · 7 · 138	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,138470,-6288673]	[a1,a2,a3,a4,a6]
Generators	[87:2491:1]	Generators of the group modulo torsion
j	293623352309352854879/187320324116835000	j-invariant
L	4.2863873932156	L(r)(E,1)/r!
Ω	0.18309384314007	Real period
R	0.48772659870569	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21840cg5 87360ck5 8190n6 13650z6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730x6

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	-	-6	-4	-8	-10	0	-2	-6	12	8	-2	4	-2	-4	8	-14	16	-4	-6	-6

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Quadratic twists for elliptic curve 2730x6

-4	8	-3	5	-7	13
21840cg5	87360ck5	8190n6	13650z6	19110cp6	35490a5

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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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