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	1748f	Isogeny class
Conductor	1748	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-720046564096 = -1 · 28 · 19 · 236	Discriminant
Eigenvalues	2- -2 -3 -1  3  2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1363,-35489]	[a1,a2,a3,a4,a6]
Generators	[1470:12167:27]	Generators of the group modulo torsion
j	1093081751552/2812681891	j-invariant
L	1.7568190782039	L(r)(E,1)/r!
Ω	0.46528332508311	Real period
R	1.8879024709193	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	6992l2 27968b2 15732i2 43700l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1748f2

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	-3	-1	3	2	3	-	+	0	-4	-4	12	11	-9	-12	0	-7	-4	0	-7	-10	12	6	-10

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Quadratic twists for elliptic curve 1748f2

-4	8	-3	5	-7	-19	-23
6992l2	27968b2	15732i2	43700l2	85652b2	33212c2	40204d2

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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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