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
deg	4	Modular degree for the optimal curve
Δ	-7168 = -1 · 210 · 7	Discriminant
Eigenvalues	2+  2 -4 7-  0  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,0,-4]	[a1,a2,a3,a4,a6]
j	-4/7	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	112a1 448h1 504h1 1400h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 56b1

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 56b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
112a1	448h1	504h1	1400h1	392d1	6776g1	9464g1	16184a1	20216k1	29624d1	47096l1	53816a1	76664k1	94136a1	103544g1	123704b1

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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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