Cremona's table of elliptic curves

5684 = 2² · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29+	Signs for the Atkin-Lehner involutions
Class	5684a	Isogeny class
Conductor	5684	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	77571162256 = 24 · 78 · 292	Discriminant
Eigenvalues	2- -1 -1 7+ -5 -2 -7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1486,-17023]	[a1,a2,a3,a4,a6]
Generators	[-16:49:1] [-14:29:1]	Generators of the group modulo torsion
j	3937024/841	j-invariant
L	4.0556329062432	L(r)(E,1)/r!
Ω	0.780536064544	Real period
R	0.28866435450025	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22736p1 90944h1 51156j1 5684e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5684a1

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
-	-1	-1	+	-5	-2	-7	-7	-9	+	7	-7	2	4	-3	-9	-7	13	5	-4	9	9	-12	1	-2

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Quadratic twists for elliptic curve 5684a1

-4	8	-3	-7
22736p1	90944h1	51156j1	5684e1

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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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