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	32	Product of Tamagawa factors cp
Δ	426649337856 = 214 · 312 · 72	Discriminant
Eigenvalues	2+ 3-  2 7-  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9084,-331760]	[a1,a2,a3,a4,a6]
Generators	[117:455:1]	Generators of the group modulo torsion
j	6940769488/35721	j-invariant
L	4.0840139470947	L(r)(E,1)/r!
Ω	0.48917563716785	Real period
R	4.1743840420382	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4032bd2 504g2 1344j2 100800db2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032o2

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 4032o2

-4	8	-3	5	-7
4032bd2	504g2	1344j2	100800db2	28224ce2

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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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