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
deg	2	Modular degree for the optimal curve
Δ	2304 = 28 · 32	Discriminant
Eigenvalues	2+ 3- -2  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4,-4]	[a1,a2,a3,a4,a6]
j	35152/9	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	24a1 192d2 144b2 1200a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 48a1

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 48a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
24a1	192d2	144b2	1200a2	2352c2	5808o2	8112k2	13872b2	17328f2	25392g2	40368c2	46128f2	65712j2	80688e2	88752f2	106032n2

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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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