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	4	Product of Tamagawa factors cp
deg	400	Modular degree for the optimal curve
Δ	-448063 = -1 · 7 · 112 · 232	Discriminant
Eigenvalues	-1 -2 -4 7+ 11- -6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,10,-29]	[a1,a2,a3,a4,a6]
Generators	[3:4:1]	Generators of the group modulo torsion
j	109902239/448063	j-invariant
L	0.79969971196144	L(r)(E,1)/r!
Ω	1.5040080810261	Real period
R	0.53171237711425	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	28336bi1 113344k1 15939c1 44275i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1771b1

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 1771b1

-4	8	-3	5	-7	-11	-23
28336bi1	113344k1	15939c1	44275i1	12397o1	19481e1	40733j1

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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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