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	72	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-4665765888 = -1 · 212 · 34 · 73 · 41	Discriminant
Eigenvalues	2- 3+ -2 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,101,3305]	[a1,a2,a3,a4,a6]
Generators	[19:-122:1]	Generators of the group modulo torsion
j	113872553423/4665765888	j-invariant
L	3.3108093172416	L(r)(E,1)/r!
Ω	1.039933765294	Real period
R	0.17687073647989	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	13776p1 55104bj1 5166s1 43050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722m1

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 1722m1

-4	8	-3	5	-7	41
13776p1	55104bj1	5166s1	43050m1	12054bn1	70602be1

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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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