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	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-215259698549952 = -1 · 26 · 35 · 712	Discriminant
Eigenvalues	2+ 3+  4 7- -2  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,10274,-584492]	[a1,a2,a3,a4,a6]
j	15926924096/28588707	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	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4704bg1 9408bl2 14112ci1 117600gx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704h1

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 4704h1

-4	8	-3	5	-7
4704bg1	9408bl2	14112ci1	117600gx1	672b1

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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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