Cremona's table of elliptic curves

224 = 2⁵ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	224a	Isogeny class
Conductor	224	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	25088 = 29 · 72	Discriminant
Eigenvalues	2+ -2  0 7+ -4 -4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,-8]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	125000/49	j-invariant
L	1.1435250753789	L(r)(E,1)/r!
Ω	2.9056796323957	Real period
R	0.39354822969112	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	224b2 448d2 2016l2 5600u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 224a2

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	+	-4	-4	-2	-6	8	2	-4	10	-10	4	4	-2	10	-8	-8	0	-6	-16	2	18	-2

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Quadratic twists for elliptic curve 224a2

-4	8	-3	5	-7	-11	13	17	-19	-23
224b2	448d2	2016l2	5600u2	1568c2	27104x2	37856s2	64736h2	80864i2	118496e2

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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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