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	4032u	Isogeny class
Conductor	4032	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-15801827328 = -1 · 214 · 39 · 72	Discriminant
Eigenvalues	2- 3+ -2 7+  6  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,324,5616]	[a1,a2,a3,a4,a6]
j	11664/49	j-invariant
L	1.7730186344933	L(r)(E,1)/r!
Ω	0.88650931724665	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	4032d2 1008a2 4032t2 100800jz2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032u2

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

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Quadratic twists for elliptic curve 4032u2

-4	8	-3	5	-7
4032d2	1008a2	4032t2	100800jz2	28224du2

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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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