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	1690b	Isogeny class
Conductor	1690	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	21840	Modular degree for the optimal curve
Δ	-344646229622500000 = -1 · 25 · 57 · 1310	Discriminant
Eigenvalues	2+  0 5+  3  3 13+ -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-148160,35808800]	[a1,a2,a3,a4,a6]
Generators	[-2266:60457:8]	Generators of the group modulo torsion
j	-2609064081/2500000	j-invariant
L	2.1700286456331	L(r)(E,1)/r!
Ω	0.27674551523115	Real period
R	7.8412423190331	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	13520o1 54080be1 15210bs1 8450n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690b1

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 1690b1

-4	8	-3	5	-7	13
13520o1	54080be1	15210bs1	8450n1	82810bc1	1690g1

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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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