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	1690g	Isogeny class
Conductor	1690	Conductor
∏ cp	105	Product of Tamagawa factors cp
Δ	-4906742437642240 = -1 · 235 · 5 · 134	Discriminant
Eigenvalues	2-  0 5- -3 -3 13+ -4  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-76927,-8857689]	[a1,a2,a3,a4,a6]
Generators	[2259:105366:1]	Generators of the group modulo torsion
j	-1762712152495281/171798691840	j-invariant
L	3.8854675667666	L(r)(E,1)/r!
Ω	0.14254573506009	Real period
R	0.2595970549468	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	13520w2 54080f2 15210l2 8450a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690g2

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
-	0	-	-3	-3	+	-4	7	-4	-8	-10	3	-2	6	-1	-9	-4	-14	4	6	4	10	0	1	16

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Quadratic twists for elliptic curve 1690g2

-4	8	-3	5	-7	13
13520w2	54080f2	15210l2	8450a2	82810bu2	1690b2

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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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