Cremona's table of elliptic curves

2847 = 3 · 13 · 73

Field	Data	Notes
Atkin-Lehner	3- 13- 73+	Signs for the Atkin-Lehner involutions
Class	2847b	Isogeny class
Conductor	2847	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	36984981267 = 35 · 134 · 732	Discriminant
Eigenvalues	-1 3-  0 -2  0 13-  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1553,21534]	[a1,a2,a3,a4,a6]
Generators	[31:43:1]	Generators of the group modulo torsion
j	414243361428625/36984981267	j-invariant
L	2.4184305225235	L(r)(E,1)/r!
Ω	1.1263795897126	Real period
R	0.21470830478565	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	45552k2 8541d2 71175b2 37011e2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2847b2

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
-1	-	0	-2	0	-	0	0	0	-8	2	6	-6	10	-4	12	0	2	-12	8	+	-16	-4	6	-2

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Quadratic twists for elliptic curve 2847b2

-4	-3	5	13
45552k2	8541d2	71175b2	37011e2

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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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