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	32	Product of Tamagawa factors cp
Δ	-13436928 = -1 · 211 · 38	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,16,180]	[a1,a2,a3,a4,a6]
j	207646/6561	j-invariant
L	0.8428751774063	L(r)(E,1)/r!
Ω	1.6857503548126	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	24a6 192d6 144b6 1200a6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 48a6

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 48a6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
24a6	192d6	144b6	1200a6	2352c6	5808o6	8112k6	13872b6	17328f6	25392g5	40368c5	46128f5	65712j5	80688e5	88752f5	106032n5

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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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