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	4032o	Isogeny class
Conductor	4032	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	177729924169728 = 216 · 318 · 7	Discriminant
Eigenvalues	2+ 3-  2 7-  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14124,77488]	[a1,a2,a3,a4,a6]
Generators	[-34:720:1]	Generators of the group modulo torsion
j	6522128932/3720087	j-invariant
L	4.0840139470947	L(r)(E,1)/r!
Ω	0.48917563716785	Real period
R	2.0871920210191	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	4032bd3 504g4 1344j3 100800db3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032o4

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

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Quadratic twists for elliptic curve 4032o4

-4	8	-3	5	-7
4032bd3	504g4	1344j3	100800db3	28224ce3

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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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