Cremona's table of elliptic curves

224 = 2⁵ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	224b	Isogeny class
Conductor	224	Conductor
∏ cp	2	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]
j	125000/49	j-invariant
L	1.717518751596	L(r)(E,1)/r!
Ω	3.435037503192	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	224a2 448g2 2016m2 5600p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 224b2

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 224b2

-4	8	-3	5	-7	-11	13	17	-19	-23
224a2	448g2	2016m2	5600p2	1568e2	27104m2	37856l2	64736b2	80864l2	118496a2

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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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