Cremona's table of elliptic curves

56 = 2³ · 7

Field	Data	Notes
Atkin-Lehner	2- 7+	Signs for the Atkin-Lehner involutions
Class	56a	Isogeny class
Conductor	56	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	50176 = 210 · 72	Discriminant
Eigenvalues	2-  0  2 7+ -4  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19,30]	[a1,a2,a3,a4,a6]
j	740772/49	j-invariant
L	0.87454831418834	L(r)(E,1)/r!
Ω	3.4981932567533	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	112b2 448a2 504c2 1400a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 56a2

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

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Quadratic twists for elliptic curve 56a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
112b2	448a2	504c2	1400a2	392a2	6776c2	9464d2	16184d2	20216b2	29624n2	47096a2	53816c2	76664b2	94136f2	103544d2	123704d2

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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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