Cremona's table of elliptic curves

1690 = 2 · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	1690f	Isogeny class
Conductor	1690	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	125497034000 = 24 · 53 · 137	Discriminant
Eigenvalues	2- -2 5+  4  6 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5496,155440]	[a1,a2,a3,a4,a6]
j	3803721481/26000	j-invariant
L	2.0991125685099	L(r)(E,1)/r!
Ω	1.0495562842549	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	13520t1 54080bn1 15210v1 8450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690f1

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

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Quadratic twists for elliptic curve 1690f1

-4	8	-3	5	-7	13
13520t1	54080bn1	15210v1	8450g1	82810cq1	130a1

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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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