Cremona's table of elliptic curves

56 = 2³ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	56b	Isogeny class
Conductor	56	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	100352 = 211 · 72	Discriminant
Eigenvalues	2+  2 -4 7-  0  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40,-84]	[a1,a2,a3,a4,a6]
j	3543122/49	j-invariant
L	0.94801911561387	L(r)(E,1)/r!
Ω	1.8960382312277	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	112a2 448h2 504h2 1400h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 56b2

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	-4	-	0	0	-2	-2	8	2	4	-6	-2	8	-4	-10	6	4	-12	0	-14	-8	6	10	-2

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Quadratic twists for elliptic curve 56b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
112a2	448h2	504h2	1400h2	392d2	6776g2	9464g2	16184a2	20216k2	29624d2	47096l2	53816a2	76664k2	94136a2	103544g2	123704b2

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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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