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	8	Product of Tamagawa factors cp
Δ	153600 = 211 · 3 · 52	Discriminant
Eigenvalues	2+ 3+ 5-  0  4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3200,70752]	[a1,a2,a3,a4,a6]
j	1770025017602/75	j-invariant
L	1.2064449969911	L(r)(E,1)/r!
Ω	2.4128899939821	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	120a5 960l5 720c5 1200e5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240a5

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 240a5

-4	8	-3	5	-7	-11	13	17	-19	-23
120a5	960l5	720c5	1200e5	11760x5	29040o6	40560a6	69360x6	86640ba6	126960b6

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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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