Cremona's table of elliptic curves

3762 = 2 · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 19-	Signs for the Atkin-Lehner involutions
Class	3762r	Isogeny class
Conductor	3762	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-14626656 = -1 · 25 · 37 · 11 · 19	Discriminant
Eigenvalues	2- 3- -3  2 11-  0 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-59,267]	[a1,a2,a3,a4,a6]
Generators	[-1:18:1]	Generators of the group modulo torsion
j	-30664297/20064	j-invariant
L	4.6517561953766	L(r)(E,1)/r!
Ω	2.0509284026213	Real period
R	0.11340610889759	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	30096y1 120384v1 1254b1 94050bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762r1

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
-	-	-3	2	-	0	-7	-	-4	-1	-2	-3	2	-5	8	-6	0	13	-1	-8	-4	-8	-10	1	8

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Quadratic twists for elliptic curve 3762r1

-4	8	-3	5	-11	-19
30096y1	120384v1	1254b1	94050bj1	41382x1	71478bh1

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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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