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	4032q	Isogeny class
Conductor	4032	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	944961619392 = 26 · 316 · 73	Discriminant
Eigenvalues	2+ 3- -4 7- -2  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3387,-59740]	[a1,a2,a3,a4,a6]
Generators	[-32:126:1]	Generators of the group modulo torsion
j	92100460096/20253807	j-invariant
L	2.8866366722809	L(r)(E,1)/r!
Ω	0.63562086839963	Real period
R	1.5138147155494	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	4032k1 2016n2 1344e1 100800di1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032q1

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

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Quadratic twists for elliptic curve 4032q1

-4	8	-3	5	-7
4032k1	2016n2	1344e1	100800di1	28224cs1

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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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