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
deg	1344	Modular degree for the optimal curve
Δ	80318101760 = 28 · 5 · 137	Discriminant
Eigenvalues	2+  0 5+  0  0 13+  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1130,-5004]	[a1,a2,a3,a4,a6]
Generators	[-28:78:1]	Generators of the group modulo torsion
j	33076161/16640	j-invariant
L	2.0178758590114	L(r)(E,1)/r!
Ω	0.86794702660257	Real period
R	2.3248836589833	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	13520n1 54080bb1 15210bm1 8450m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690a1

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 1690a1

-4	8	-3	5	-7	13
13520n1	54080bb1	15210bm1	8450m1	82810bb1	130b1

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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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