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	4	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-1159543 = -1 · 7 · 112 · 372	Discriminant
Eigenvalues	-1  0  0 7- 11- -4  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,5,50]	[a1,a2,a3,a4,a6]
Generators	[6:13:1]	Generators of the group modulo torsion
j	16581375/1159543	j-invariant
L	2.0784058488694	L(r)(E,1)/r!
Ω	2.0934013065718	Real period
R	0.9928367973903	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	45584h1 25641g1 71225d1 19943d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2849b1

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 2849b1

-4	-3	5	-7	-11	37
45584h1	25641g1	71225d1	19943d1	31339a1	105413g1

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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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