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
Δ	-2.3683908558694E+22	Discriminant
Eigenvalues	2+  0 5+  3  3 13+ -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-13000610,-19499343980]	[a1,a2,a3,a4,a6]
Generators	[681434914202069776718880577240578:-568945279770478043684663213608522541:978679125304605392399970776]	Generators of the group modulo torsion
j	-1762712152495281/171798691840	j-invariant
L	2.1700286456331	L(r)(E,1)/r!
Ω	0.039535073604449	Real period
R	54.888696233232	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	13520o2 54080be2 15210bs2 8450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690b2

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 1690b2

-4	8	-3	5	-7	13
13520o2	54080be2	15210bs2	8450n2	82810bc2	1690g2

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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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