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	1	Product of Tamagawa factors cp
Δ	-48 = -1 · 24 · 3	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1,0]	[a1,a2,a3,a4,a6]
j	2048/3	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	2	Number of elements in the torsion subgroup
Twists	24a4 192d1 144b1 1200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 48a4

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 48a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
24a4	192d1	144b1	1200a1	2352c1	5808o1	8112k1	13872b1	17328f1	25392g1	40368c1	46128f1	65712j1	80688e1	88752f1	106032n1

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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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