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	4704h	Isogeny class
Conductor	4704	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	9760113212387328 = 212 · 310 · 79	Discriminant
Eigenvalues	2+ 3+  4 7- -2  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-73761,-6046767]	[a1,a2,a3,a4,a6]
j	92100460096/20253807	j-invariant
L	2.3538823031971	L(r)(E,1)/r!
Ω	0.29423528789963	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4704bg2 9408bl1 14112ci2 117600gx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704h2

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

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Quadratic twists for elliptic curve 4704h2

-4	8	-3	5	-7
4704bg2	9408bl1	14112ci2	117600gx2	672b2

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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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