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	4704n	Isogeny class
Conductor	4704	Conductor
∏ cp	12	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	[10:6:1]	Generators of the group modulo torsion
j	82881856/27	j-invariant
L	3.9143106346429	L(r)(E,1)/r!
Ω	2.8420800189303	Real period
R	0.45908989291536	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	4704w1 9408j2 14112bz1 117600er1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704n1

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 4704n1

-4	8	-3	5	-7
4704w1	9408j2	14112bz1	117600er1	4704e1

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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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