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	18	Product of Tamagawa factors cp
Δ	23261664552 = 23 · 3 · 73 · 414	Discriminant
Eigenvalues	2- 3+ -2 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-43939,3526745]	[a1,a2,a3,a4,a6]
Generators	[121:-54:1]	Generators of the group modulo torsion
j	9381555148655972017/23261664552	j-invariant
L	3.3108093172416	L(r)(E,1)/r!
Ω	1.039933765294	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	13776p3 55104bj4 5166s3 43050m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722m4

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 1722m4

-4	8	-3	5	-7	41
13776p3	55104bj4	5166s3	43050m4	12054bn3	70602be4

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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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