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	8	Product of Tamagawa factors cp
Δ	1024192512 = 212 · 36 · 73	Discriminant
Eigenvalues	2- 3+ -2 7-  2  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-289,-1007]	[a1,a2,a3,a4,a6]
Generators	[-9:28:1]	Generators of the group modulo torsion
j	1906624/729	j-invariant
L	2.8151222075076	L(r)(E,1)/r!
Ω	1.1955210417002	Real period
R	1.1773620493973	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	4704n2 9408be1 14112u2 117600cu2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704w2

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 4704w2

-4	8	-3	5	-7
4704n2	9408be1	14112u2	117600cu2	4704bc2

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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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