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	1771d	Isogeny class
Conductor	1771	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	1771 = 7 · 11 · 23	Discriminant
Eigenvalues	-1 -1 -1 7- 11+ -1  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6,-8]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	24137569/1771	j-invariant
L	1.4689869200006	L(r)(E,1)/r!
Ω	3.0619129723998	Real period
R	0.47976116017736	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	28336w1 113344bx1 15939i1 44275a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1771d1

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	-1	-1	-	+	-1	0	5	-	6	0	8	-7	-6	1	8	-12	10	-11	14	5	-6	-13	-3	1

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Quadratic twists for elliptic curve 1771d1

-4	8	-3	5	-7	-11	-23
28336w1	113344bx1	15939i1	44275a1	12397g1	19481c1	40733d1

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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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