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
deg	2	Modular degree for the optimal curve
Δ	-1792 = -1 · 28 · 7	Discriminant
Eigenvalues	2-  0  2 7+ -4  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1,2]	[a1,a2,a3,a4,a6]
j	432/7	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	112b1 448a1 504c1 1400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 56a1

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 56a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
112b1	448a1	504c1	1400a1	392a1	6776c1	9464d1	16184d1	20216b1	29624n1	47096a1	53816c1	76664b1	94136f1	103544d1	123704d1

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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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