Cremona's table of elliptic curves

4032 = 2⁶ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+	Signs for the Atkin-Lehner involutions
Class	4032b	Isogeny class
Conductor	4032	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-987614208 = -1 · 210 · 39 · 72	Discriminant
Eigenvalues	2+ 3+ -2 7+ -2 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-216,-1944]	[a1,a2,a3,a4,a6]
Generators	[25:91:1]	Generators of the group modulo torsion
j	-55296/49	j-invariant
L	3.0821772670347	L(r)(E,1)/r!
Ω	0.60048411363668	Real period
R	2.5664103321304	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	4032y1 504d1 4032a1 100800v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032b1

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
+	+	-2	+	-2	-2	6	4	6	0	-4	-10	2	4	4	12	-12	-6	4	-14	-2	-8	16	-6	-18

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Quadratic twists for elliptic curve 4032b1

-4	8	-3	5	-7
4032y1	504d1	4032a1	100800v1	28224n1

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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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