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	96	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-801531494400 = -1 · 224 · 3 · 52 · 72 · 13	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-370,43007]	[a1,a2,a3,a4,a6]
Generators	[-23:211:1]	Generators of the group modulo torsion
j	-5602762882081/801531494400	j-invariant
L	4.2863873932156	L(r)(E,1)/r!
Ω	0.73237537256027	Real period
R	0.97545319741138	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840cg1 87360ck1 8190n1 13650z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730x1

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 2730x1

-4	8	-3	5	-7	13
21840cg1	87360ck1	8190n1	13650z1	19110cp1	35490a1

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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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