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	1722g	Isogeny class
Conductor	1722	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	2736	Modular degree for the optimal curve
Δ	-132944060214 = -1 · 2 · 39 · 72 · 413	Discriminant
Eigenvalues	2+ 3-  3 7-  0 -1 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2082,-40718]	[a1,a2,a3,a4,a6]
j	-997392270041497/132944060214	j-invariant
L	2.1048106769255	L(r)(E,1)/r!
Ω	0.35080177948758	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13776g1 55104r1 5166bg1 43050bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722g1

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
+	-	3	-	0	-1	-3	-1	6	0	11	8	-	-10	0	12	-15	8	11	-3	-13	8	9	-15	8

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Quadratic twists for elliptic curve 1722g1

-4	8	-3	5	-7	41
13776g1	55104r1	5166bg1	43050bh1	12054d1	70602d1

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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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