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	5684f	Isogeny class
Conductor	5684	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-873426176 = -1 · 28 · 76 · 29	Discriminant
Eigenvalues	2- -1 -3 7-  3 -5  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-212,-1784]	[a1,a2,a3,a4,a6]
Generators	[26:98:1]	Generators of the group modulo torsion
j	-35152/29	j-invariant
L	2.4815935177697	L(r)(E,1)/r!
Ω	0.60417170315306	Real period
R	0.68457181537928	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	22736v1 90944bn1 51156be1 116b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5684f1

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	-3	-	3	-5	6	4	-6	+	-5	8	0	-1	3	3	-6	-2	8	6	16	11	-6	12	-8

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Quadratic twists for elliptic curve 5684f1

-4	8	-3	-7
22736v1	90944bn1	51156be1	116b1

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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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