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	144	Product of Tamagawa factors cp
Δ	113914350144 = 26 · 32 · 76 · 412	Discriminant
Eigenvalues	2- 3+ -2 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2779,52841]	[a1,a2,a3,a4,a6]
Generators	[-47:310:1]	Generators of the group modulo torsion
j	2373554016849457/113914350144	j-invariant
L	3.3108093172416	L(r)(E,1)/r!
Ω	1.039933765294	Real period
R	0.35374147295978	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13776p2 55104bj2 5166s2 43050m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1722m2

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 1722m2

-4	8	-3	5	-7	41
13776p2	55104bj2	5166s2	43050m2	12054bn2	70602be2

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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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