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	48	Product of Tamagawa factors cp
Δ	-37276936195969600 = -1 · 26 · 52 · 1312	Discriminant
Eigenvalues	2- -2 5+  4  6 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,19009,-9232679]	[a1,a2,a3,a4,a6]
j	157376536199/7722894400	j-invariant
L	2.0991125685099	L(r)(E,1)/r!
Ω	0.17492604737582	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	13520t4 54080bn4 15210v4 8450g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690f4

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 1690f4

-4	8	-3	5	-7	13
13520t4	54080bn4	15210v4	8450g4	82810cq4	130a4

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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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