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	4032s	Isogeny class
Conductor	4032	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	84672 = 26 · 33 · 72	Discriminant
Eigenvalues	2- 3+  0 7+ -4 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-195,-1048]	[a1,a2,a3,a4,a6]
j	474552000/49	j-invariant
L	1.2775961447258	L(r)(E,1)/r!
Ω	1.2775961447258	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	4032v1 2016i2 4032r1 100800jx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032s1

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	+	-4	-2	-4	0	4	-4	8	2	4	8	8	4	-8	2	8	12	6	8	-16	12	-2

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Quadratic twists for elliptic curve 4032s1

-4	8	-3	5	-7
4032v1	2016i2	4032r1	100800jx1	28224dn1

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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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