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	4704f	Isogeny class
Conductor	4704	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	67765824 = 26 · 32 · 76	Discriminant
Eigenvalues	2+ 3+ -2 7-  4  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-114,-216]	[a1,a2,a3,a4,a6]
j	21952/9	j-invariant
L	1.5134867381822	L(r)(E,1)/r!
Ω	1.5134867381822	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4704bf1 9408bg2 14112ca1 117600ha1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704f1

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	-	4	2	6	4	0	2	-4	-2	-2	4	-8	10	4	-6	4	-16	6	4	-12	-10	14

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Quadratic twists for elliptic curve 4704f1

-4	8	-3	5	-7
4704bf1	9408bg2	14112ca1	117600ha1	96a1

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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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