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	1690h	Isogeny class
Conductor	1690	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-6760 = -1 · 23 · 5 · 132	Discriminant
Eigenvalues	2- -2 5-  1 -3 13+ -6 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10,12]	[a1,a2,a3,a4,a6]
Generators	[2:0:1]	Generators of the group modulo torsion
j	-658489/40	j-invariant
L	3.2111547605296	L(r)(E,1)/r!
Ω	4.1502892923459	Real period
R	0.25790609877499	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	13520ba1 54080m1 15210i1 8450f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690h1

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	-	1	-3	+	-6	-5	0	0	4	-11	-6	2	3	-9	0	8	16	-6	-14	-16	6	-9	10

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Quadratic twists for elliptic curve 1690h1

-4	8	-3	5	-7	13
13520ba1	54080m1	15210i1	8450f1	82810cc1	1690c1

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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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