Cremona's table of elliptic curves

1722 = 2 · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	1722m	Isogeny class
Conductor	1722	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	13619826605784 = 23 · 3 · 712 · 41	Discriminant
Eigenvalues	2- 3+ -2 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7699,-193159]	[a1,a2,a3,a4,a6]
Generators	[-59:274:1]	Generators of the group modulo torsion
j	50469638798675377/13619826605784	j-invariant
L	3.3108093172416	L(r)(E,1)/r!
Ω	0.51996688264702	Real period
R	0.70748294591957	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	13776p4 55104bj3 5166s4 43050m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722m3

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
-	+	-2	-	-4	2	-2	4	-8	-2	4	-10	+	4	-8	-2	0	-6	-8	-12	-14	-8	16	6	-2

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Quadratic twists for elliptic curve 1722m3

-4	8	-3	5	-7	41
13776p4	55104bj3	5166s4	43050m3	12054bn4	70602be3

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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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