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
deg	1680	Modular degree for the optimal curve
Δ	-71402500000 = -1 · 25 · 57 · 134	Discriminant
Eigenvalues	2-  0 5- -3 -3 13+ -4  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-877,16501]	[a1,a2,a3,a4,a6]
Generators	[-29:144:1]	Generators of the group modulo torsion
j	-2609064081/2500000	j-invariant
L	3.8854675667666	L(r)(E,1)/r!
Ω	0.9978201454206	Real period
R	0.037085293563829	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	13520w1 54080f1 15210l1 8450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690g1

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 1690g1

-4	8	-3	5	-7	13
13520w1	54080f1	15210l1	8450a1	82810bu1	1690b1

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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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