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	2847a	Isogeny class
Conductor	2847	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-4109442363 = -1 · 33 · 134 · 732	Discriminant
Eigenvalues	-1 3+  0  4 -2 13+  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-113,-3166]	[a1,a2,a3,a4,a6]
Generators	[17:5:1]	Generators of the group modulo torsion
j	-159661140625/4109442363	j-invariant
L	2.0052117920842	L(r)(E,1)/r!
Ω	0.60170952136844	Real period
R	3.332524616735	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	45552l2 8541c2 71175o2 37011a2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2847a2

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	4	-2	+	4	-4	-4	0	-4	2	-6	12	-2	-4	-6	-2	12	0	+	-8	6	-18	10

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Quadratic twists for elliptic curve 2847a2

-4	-3	5	13
45552l2	8541c2	71175o2	37011a2

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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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