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	4	Product of Tamagawa factors cp
Δ	18432 = 211 · 32	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-384,2772]	[a1,a2,a3,a4,a6]
j	3065617154/9	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	4	Number of elements in the torsion subgroup
Twists	24a5 192d5 144b5 1200a5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 48a5

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 48a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
24a5	192d5	144b5	1200a5	2352c5	5808o5	8112k5	13872b5	17328f5	25392g6	40368c6	46128f6	65712j6	80688e6	88752f6	106032n6

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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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