Cremona's table of elliptic curves

1748 = 2² · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 19+ 23+	Signs for the Atkin-Lehner involutions
Class	1748a	Isogeny class
Conductor	1748	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-132848 = -1 · 24 · 192 · 23	Discriminant
Eigenvalues	2- -1 -4 -2 -6 -3 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-90,361]	[a1,a2,a3,a4,a6]
Generators	[-9:19:1] [0:19:1]	Generators of the group modulo torsion
j	-5095042816/8303	j-invariant
L	2.4210142972587	L(r)(E,1)/r!
Ω	3.2846749033435	Real period
R	0.12284393273303	Regulator
r	2	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992v1 27968j1 15732h1 43700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1748a1

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
-	-1	-4	-2	-6	-3	-4	+	+	-5	-1	4	5	-10	5	-12	-4	-4	-2	-13	5	16	-6	-16	-12

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Quadratic twists for elliptic curve 1748a1

-4	8	-3	5	-7	-19	-23
6992v1	27968j1	15732h1	43700h1	85652g1	33212a1	40204h1

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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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