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	4032z	Isogeny class
Conductor	4032	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-5350883328 = -1 · 220 · 36 · 7	Discriminant
Eigenvalues	2- 3-  0 7+  0  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-300,4048]	[a1,a2,a3,a4,a6]
Generators	[-4:72:1]	Generators of the group modulo torsion
j	-15625/28	j-invariant
L	3.5850068046031	L(r)(E,1)/r!
Ω	1.2133191995829	Real period
R	1.4773551781903	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	4032l1 1008i1 448f1 100800mz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032z1

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
-	-	0	+	0	4	-6	2	0	-6	4	-2	-6	8	-12	6	6	-8	-4	0	2	-8	6	6	-10

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Quadratic twists for elliptic curve 4032z1

-4	8	-3	5	-7
4032l1	1008i1	448f1	100800mz1	28224fc1

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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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