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	5684c	Isogeny class
Conductor	5684	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	3672	Modular degree for the optimal curve
Δ	14990845184 = 28 · 74 · 293	Discriminant
Eigenvalues	2- -2 -3 7+  0 -1  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1437,-20609]	[a1,a2,a3,a4,a6]
Generators	[-22:29:1]	Generators of the group modulo torsion
j	534274048/24389	j-invariant
L	1.9361522955475	L(r)(E,1)/r!
Ω	0.77756307614258	Real period
R	0.83000867494574	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	22736s1 90944d1 51156e1 5684k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5684c1

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
-	-2	-3	+	0	-1	0	-4	0	-	2	8	-6	2	0	9	0	8	-4	3	-16	8	3	12	-10

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Quadratic twists for elliptic curve 5684c1

-4	8	-3	-7
22736s1	90944d1	51156e1	5684k1

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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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