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	4704o	Isogeny class
Conductor	4704	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-677376 = -1 · 29 · 33 · 72	Discriminant
Eigenvalues	2+ 3- -3 7-  1  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-72,216]	[a1,a2,a3,a4,a6]
Generators	[6:-6:1]	Generators of the group modulo torsion
j	-1668296/27	j-invariant
L	3.8164764696592	L(r)(E,1)/r!
Ω	2.8745523160393	Real period
R	0.22127946952321	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	4704g1 9408cf1 14112cf1 117600eo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704o1

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	-	1	4	-4	0	-8	-7	11	4	4	2	-2	-11	7	-10	-10	-6	6	-11	11	-6	-7

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Quadratic twists for elliptic curve 4704o1

-4	8	-3	5	-7
4704g1	9408cf1	14112cf1	117600eo1	4704c1

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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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