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	16	Product of Tamagawa factors cp
Δ	-344646229622500 = -1 · 22 · 54 · 1310	Discriminant
Eigenvalues	2+  0 5+  0  0 13+  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-11270,-1002104]	[a1,a2,a3,a4,a6]
Generators	[868:24916:1]	Generators of the group modulo torsion
j	-32798729601/71402500	j-invariant
L	2.0178758590114	L(r)(E,1)/r!
Ω	0.21698675665064	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	13520n4 54080bb3 15210bm4 8450m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1690a4

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 1690a4

-4	8	-3	5	-7	13
13520n4	54080bb3	15210bm4	8450m4	82810bb3	130b4

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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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