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	1690a	Isogeny class
Conductor	1690	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1254970340 = 22 · 5 · 137	Discriminant
Eigenvalues	2+  0 5+  0  0 13+  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-234350,-43607680]	[a1,a2,a3,a4,a6]
Generators	[1223004:20173639:1728]	Generators of the group modulo torsion
j	294889639316481/260	j-invariant
L	2.0178758590114	L(r)(E,1)/r!
Ω	0.21698675665064	Real period
R	9.2995346359331	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13520n3 54080bb4 15210bm3 8450m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690a3

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	+	0	0	+	2	8	-4	-2	4	-6	-10	0	-8	6	-8	-2	-4	12	-10	-8	-12	-10	14

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Quadratic twists for elliptic curve 1690a3

-4	8	-3	5	-7	13
13520n3	54080bb4	15210bm3	8450m3	82810bb4	130b3

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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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