Cremona's table of elliptic curves

5698 = 2 · 7 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11- 37+	Signs for the Atkin-Lehner involutions
Class	5698a	Isogeny class
Conductor	5698	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-561218812 = -1 · 22 · 7 · 114 · 372	Discriminant
Eigenvalues	2+ -2  2 7+ 11-  2  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2985,-63016]	[a1,a2,a3,a4,a6]
j	-2940001530995593/561218812	j-invariant
L	1.2918316573768	L(r)(E,1)/r!
Ω	0.32295791434419	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45584l1 51282bc1 39886h1 62678j1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5698a1

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

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Quadratic twists for elliptic curve 5698a1

-4	-3	-7	-11
45584l1	51282bc1	39886h1	62678j1

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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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