Cremona's table of elliptic curves

4704 = 2⁵ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	4704w	Isogeny class
Conductor	4704	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	592704 = 26 · 33 · 73	Discriminant
Eigenvalues	2- 3+ -2 7-  2  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-254,-1476]	[a1,a2,a3,a4,a6]
Generators	[19:14:1]	Generators of the group modulo torsion
j	82881856/27	j-invariant
L	2.8151222075076	L(r)(E,1)/r!
Ω	1.1955210417002	Real period
R	2.3547240987946	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	4704n1 9408be2 14112u1 117600cu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704w1

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
-	+	-2	-	2	0	-2	0	-2	6	-4	6	2	0	0	-6	12	-12	12	10	-12	-12	12	-14	12

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Quadratic twists for elliptic curve 4704w1

-4	8	-3	5	-7
4704n1	9408be2	14112u1	117600cu1	4704bc1

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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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