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	4	Product of Tamagawa factors cp
Δ	-33592320 = -1 · 210 · 38 · 5	Discriminant
Eigenvalues	2+ 3+ 5-  0  4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,80,-80]	[a1,a2,a3,a4,a6]
j	54607676/32805	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	2	Number of elements in the torsion subgroup
Twists	120a4 960l4 720c4 1200e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240a4

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 240a4

-4	8	-3	5	-7	-11	13	17	-19	-23
120a4	960l4	720c4	1200e4	11760x4	29040o3	40560a3	69360x3	86640ba3	126960b3

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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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