Cremona's table of elliptic curves

4774 = 2 · 7 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 11- 31-	Signs for the Atkin-Lehner involutions
Class	4774l	Isogeny class
Conductor	4774	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-41170976 = -1 · 25 · 73 · 112 · 31	Discriminant
Eigenvalues	2- -3 -3 7- 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-54,357]	[a1,a2,a3,a4,a6]
Generators	[19:-87:1]	Generators of the group modulo torsion
j	-17113674033/41170976	j-invariant
L	2.8059176788753	L(r)(E,1)/r!
Ω	1.8037229421479	Real period
R	0.05185418841791	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	38192m1 42966p1 119350h1 33418bk1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4774l1

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
-	-3	-3	-	-	-2	-6	4	-1	-3	-	10	-4	4	7	6	6	-4	1	-4	7	-13	-3	-7	-2

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Quadratic twists for elliptic curve 4774l1

-4	-3	5	-7	-11
38192m1	42966p1	119350h1	33418bk1	52514j1

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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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