Cremona's table of elliptic curves

5704 = 2³ · 23 · 31

Field	Data	Notes
Atkin-Lehner	2- 23- 31+	Signs for the Atkin-Lehner involutions
Class	5704a	Isogeny class
Conductor	5704	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	182528 = 28 · 23 · 31	Discriminant
Eigenvalues	2-  0  2  4 -4 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-239,-1422]	[a1,a2,a3,a4,a6]
Generators	[89:826:1]	Generators of the group modulo torsion
j	5897629008/713	j-invariant
L	4.5142544966956	L(r)(E,1)/r!
Ω	1.214236349883	Real period
R	3.7177724889643	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	11408a1 45632f1 51336e1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5704a1

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

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Quadratic twists for elliptic curve 5704a1

-4	8	-3
11408a1	45632f1	51336e1

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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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