Cremona's table of elliptic curves

4977 = 3² · 7 · 79

Field	Data	Notes
Atkin-Lehner	3- 7- 79+	Signs for the Atkin-Lehner involutions
Class	4977c	Isogeny class
Conductor	4977	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	18514872999 = 314 · 72 · 79	Discriminant
Eigenvalues	-1 3- -2 7-  0  6  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3686,-84954]	[a1,a2,a3,a4,a6]
Generators	[-34:30:1]	Generators of the group modulo torsion
j	7595418586393/25397631	j-invariant
L	2.1909329621119	L(r)(E,1)/r!
Ω	0.61285430921432	Real period
R	1.787482709325	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	79632x2 1659b2 124425d2 34839i2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4977c2

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	-	-2	-	0	6	0	-6	-4	-2	-2	10	0	4	-8	-6	8	0	0	0	14	+	-6	-6	14

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Quadratic twists for elliptic curve 4977c2

-4	-3	5	-7
79632x2	1659b2	124425d2	34839i2

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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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