Cremona's table of elliptic curves

4949 = 7² · 101

Field	Data	Notes
Atkin-Lehner	7+ 101+	Signs for the Atkin-Lehner involutions
Class	4949a	Isogeny class
Conductor	4949	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2352	Modular degree for the optimal curve
Δ	-582244901 = -1 · 78 · 101	Discriminant
Eigenvalues	-1  1 -3 7+  4 -1 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1422,-20791]	[a1,a2,a3,a4,a6]
Generators	[446:1953:8]	Generators of the group modulo torsion
j	-55164193/101	j-invariant
L	2.2302706497594	L(r)(E,1)/r!
Ω	0.38868288311219	Real period
R	5.738021267882	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	79184p1 44541b1 123725a1 4949f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4949a1

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	1	-3	+	4	-1	-2	2	-6	4	8	-5	2	0	10	2	0	10	-3	-6	-8	-4	17	-6	-2

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Quadratic twists for elliptic curve 4949a1

-4	-3	5	-7
79184p1	44541b1	123725a1	4949f1

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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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