Cremona's table of elliptic curves

2849 = 7 · 11 · 37

Field	Data	Notes
Atkin-Lehner	7- 11- 37+	Signs for the Atkin-Lehner involutions
Class	2849b	Isogeny class
Conductor	2849	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	26544133 = 72 · 114 · 37	Discriminant
Eigenvalues	-1  0  0 7- 11- -4  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-180,938]	[a1,a2,a3,a4,a6]
Generators	[4:14:1]	Generators of the group modulo torsion
j	641619140625/26544133	j-invariant
L	2.0784058488694	L(r)(E,1)/r!
Ω	2.0934013065718	Real period
R	0.49641839869515	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	45584h2 25641g2 71225d2 19943d2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2849b2

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

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Quadratic twists for elliptic curve 2849b2

-4	-3	5	-7	-11	37
45584h2	25641g2	71225d2	19943d2	31339a2	105413g2

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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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