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	2730bb	Isogeny class
Conductor	2730	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	19377540 = 22 · 32 · 5 · 72 · 133	Discriminant
Eigenvalues	2- 3- 5- 7+  2 13+ -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2055,35685]	[a1,a2,a3,a4,a6]
j	959781554388721/19377540	j-invariant
L	3.9991065048223	L(r)(E,1)/r!
Ω	1.9995532524112	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	21840bm1 87360i1 8190h1 13650i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730bb1

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

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Quadratic twists for elliptic curve 2730bb1

-4	8	-3	5	-7	13
21840bm1	87360i1	8190h1	13650i1	19110bt1	35490bd1

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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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