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	4032bi	Isogeny class
Conductor	4032	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	2939328 = 26 · 38 · 7	Discriminant
Eigenvalues	2- 3-  2 7-  0 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-759,8048]	[a1,a2,a3,a4,a6]
j	1036433728/63	j-invariant
L	2.405381429732	L(r)(E,1)/r!
Ω	2.405381429732	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4032bc1 2016h3 1344n1 100800ky1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032bi1

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

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Quadratic twists for elliptic curve 4032bi1

-4	8	-3	5	-7
4032bc1	2016h3	1344n1	100800ky1	28224fz1

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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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