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	28224b	Isogeny class
Conductor	28224	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-4148928 = -1 · 26 · 33 · 74	Discriminant
Eigenvalues	2+ 3+  0 7+  0  7  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,98]	[a1,a2,a3,a4,a6]
Generators	[7:21:1]	Generators of the group modulo torsion
j	0	j-invariant
L	6.163079798909	L(r)(E,1)/r!
Ω	1.9590912388547	Real period
R	0.52431451180668	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	28224cx1 441b1 28224b2 28224k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224b1

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
+	+	0	+	0	7	0	7	0	0	-7	1	0	-5	0	0	0	-14	-11	0	-7	-13	0	0	14

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Quadratic twists for elliptic curve 28224b1

-4	8	-3	-7
28224cx1	441b1	28224b2	28224k1

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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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