Cremona's table of elliptic curves

28224 = 2⁶ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	28224cf	Isogeny class
Conductor	28224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	27653197824 = 212 · 39 · 73	Discriminant
Eigenvalues	2+ 3- -2 7-  2  0  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9156,337120]	[a1,a2,a3,a4,a6]
Generators	[-28:756:1]	Generators of the group modulo torsion
j	82881856/27	j-invariant
L	4.8247701554543	L(r)(E,1)/r!
Ω	1.1602743090898	Real period
R	1.0395753223303	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	28224ch2 14112u1 9408be2 28224bt2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224cf2

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

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Quadratic twists for elliptic curve 28224cf2

-4	8	-3	-7
28224ch2	14112u1	9408be2	28224bt2

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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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