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	1748c	Isogeny class
Conductor	1748	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-928873216 = -1 · 28 · 193 · 232	Discriminant
Eigenvalues	2-  0  1 -1 -1  4 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3992,97092]	[a1,a2,a3,a4,a6]
Generators	[32:46:1]	Generators of the group modulo torsion
j	-27482443554816/3628411	j-invariant
L	2.9211231289187	L(r)(E,1)/r!
Ω	1.5142015891939	Real period
R	0.32152512472199	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992n1 27968n1 15732b1 43700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1748c1

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
-	0	1	-1	-1	4	-5	+	-	-4	0	-4	6	-5	3	-4	-6	-11	2	12	-15	-12	-4	-12	12

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Quadratic twists for elliptic curve 1748c1

-4	8	-3	5	-7	-19	-23
6992n1	27968n1	15732b1	43700b1	85652j1	33212e1	40204f1

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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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