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	4704r	Isogeny class
Conductor	4704	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-438939648 = -1 · 212 · 37 · 72	Discriminant
Eigenvalues	2- 3+  0 7-  2 -1  2  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-93,-1035]	[a1,a2,a3,a4,a6]
Generators	[23:92:1]	Generators of the group modulo torsion
j	-448000/2187	j-invariant
L	3.2802912562903	L(r)(E,1)/r!
Ω	0.6941616861526	Real period
R	2.3627717588905	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4704k1 9408z1 14112o1 117600cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704r1

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
-	+	0	-	2	-1	2	5	-6	-8	-3	-9	-2	-1	8	6	6	2	5	-4	11	5	0	-12	-18

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Quadratic twists for elliptic curve 4704r1

-4	8	-3	5	-7
4704k1	9408z1	14112o1	117600cv1	4704y1

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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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