Cremona's table of elliptic curves

240 = 2⁴ · 3 · 5

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5-	Signs for the Atkin-Lehner involutions
Class	240a	Isogeny class
Conductor	240	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2400000000 = -1 · 211 · 3 · 58	Discriminant
Eigenvalues	2+ 3+ 5-  0  4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-80,2400]	[a1,a2,a3,a4,a6]
j	-27995042/1171875	j-invariant
L	1.2064449969911	L(r)(E,1)/r!
Ω	1.2064449969911	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	120a6 960l6 720c6 1200e6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240a6

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
+	+	-	0	4	6	-6	4	0	-2	8	-2	-6	-12	-8	6	-12	14	-4	-8	-6	8	12	10	2

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Quadratic twists for elliptic curve 240a6

-4	8	-3	5	-7	-11	13	17	-19	-23
120a6	960l6	720c6	1200e6	11760x6	29040o5	40560a5	69360x5	86640ba5	126960b5

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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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