Cremona's table of elliptic curves

1776 = 2⁴ · 3 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 37-	Signs for the Atkin-Lehner involutions
Class	1776d	Isogeny class
Conductor	1776	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	800	Modular degree for the optimal curve
Δ	-18413568 = -1 · 211 · 35 · 37	Discriminant
Eigenvalues	2+ 3- -4  1  3 -5  7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-200,1044]	[a1,a2,a3,a4,a6]
Generators	[10:-12:1]	Generators of the group modulo torsion
j	-434163602/8991	j-invariant
L	2.8947913285571	L(r)(E,1)/r!
Ω	2.1786071104161	Real period
R	0.066436745632492	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	888a1 7104n1 5328g1 44400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1776d1

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
+	-	-4	1	3	-5	7	-5	-1	-8	-6	-	-2	-12	2	-1	4	14	-14	-4	-11	-10	-5	-9	-10

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Quadratic twists for elliptic curve 1776d1

-4	8	-3	5	-7	37
888a1	7104n1	5328g1	44400d1	87024w1	65712k1

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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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