Cremona's table of elliptic curves

1771 = 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	7+ 11- 23-	Signs for the Atkin-Lehner involutions
Class	1771b	Isogeny class
Conductor	1771	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	16500407 = 72 · 114 · 23	Discriminant
Eigenvalues	-1 -2 -4 7+ 11- -6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-105,-374]	[a1,a2,a3,a4,a6]
Generators	[-7:9:1]	Generators of the group modulo torsion
j	128100283921/16500407	j-invariant
L	0.79969971196144	L(r)(E,1)/r!
Ω	1.5040080810261	Real period
R	0.26585618855712	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	28336bi2 113344k2 15939c2 44275i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1771b2

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	-2	-4	+	-	-6	4	-4	-	-6	10	10	10	-4	-2	6	-6	-4	4	0	-2	-8	-16	0	-12

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Quadratic twists for elliptic curve 1771b2

-4	8	-3	5	-7	-11	-23
28336bi2	113344k2	15939c2	44275i2	12397o2	19481e2	40733j2

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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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