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	2730h	Isogeny class
Conductor	2730	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	7452900 = 22 · 32 · 52 · 72 · 132	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-182,864]	[a1,a2,a3,a4,a6]
Generators	[-2:36:1]	Generators of the group modulo torsion
j	672451615081/7452900	j-invariant
L	2.2874764991882	L(r)(E,1)/r!
Ω	2.3586037683917	Real period
R	0.484921742652	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	21840cc2 87360cp2 8190bh2 13650cn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730h2

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
+	+	-	-	0	+	-2	-4	4	-2	0	-6	-6	0	-12	-10	-4	10	4	0	2	16	-12	18	2

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Quadratic twists for elliptic curve 2730h2

-4	8	-3	5	-7	13
21840cc2	87360cp2	8190bh2	13650cn2	19110w2	35490bz2

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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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