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	28224es	Isogeny class
Conductor	28224	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-806887666368 = -1 · 26 · 37 · 78	Discriminant
Eigenvalues	2- 3- -2 7+  2 -1  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4116,110446]	[a1,a2,a3,a4,a6]
Generators	[-49:441:1]	Generators of the group modulo torsion
j	-28672/3	j-invariant
L	4.6411585834326	L(r)(E,1)/r!
Ω	0.87121562389464	Real period
R	0.887870246305	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28224bd1 7056bm1 9408cm1 28224fq1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224es1

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	-1	0	1	0	4	-9	-3	10	5	-6	12	12	-10	-5	-6	-3	1	-6	-16	-6

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Quadratic twists for elliptic curve 28224es1

-4	8	-3	-7
28224bd1	7056bm1	9408cm1	28224fq1

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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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