Cremona's table of elliptic curves

1634 = 2 · 19 · 43

Field	Data	Notes
Atkin-Lehner	2- 19+ 43-	Signs for the Atkin-Lehner involutions
Class	1634d	Isogeny class
Conductor	1634	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-1151172608 = -1 · 215 · 19 · 432	Discriminant
Eigenvalues	2-  1 -2 -1 -2 -3  3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-164,1808]	[a1,a2,a3,a4,a6]
Generators	[32:156:1]	Generators of the group modulo torsion
j	-488001047617/1151172608	j-invariant
L	4.0275833555751	L(r)(E,1)/r!
Ω	1.367359057573	Real period
R	0.098183997667343	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	13072f1 52288c1 14706h1 40850a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1634d1

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
-	1	-2	-1	-2	-3	3	+	-3	-1	0	-2	-8	-	-4	5	-1	-4	-5	4	-1	8	-6	8	16

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Quadratic twists for elliptic curve 1634d1

-4	8	-3	5	-7	-19	-43
13072f1	52288c1	14706h1	40850a1	80066h1	31046g1	70262c1

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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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