Cremona's table of elliptic curves

48 = 2⁴ · 3

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	48a	Isogeny class
Conductor	48	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	82944 = 210 · 34	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-24,36]	[a1,a2,a3,a4,a6]
j	1556068/81	j-invariant
L	0.8428751774063	L(r)(E,1)/r!
Ω	3.3715007096252	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	24a2 192d4 144b3 1200a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 48a3

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	-2	2	4	8	6	-8	6	-6	-4	0	-2	-4	-2	4	-8	10	8	4	-6	2

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Quadratic twists for elliptic curve 48a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
24a2	192d4	144b3	1200a4	2352c3	5808o3	8112k4	13872b4	17328f3	25392g3	40368c3	46128f3	65712j3	80688e3	88752f3	106032n3

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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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