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	240b	Isogeny class
Conductor	240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-6291456000 = -1 · 224 · 3 · 53	Discriminant
Eigenvalues	2- 3+ 5+  4  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-216,4080]	[a1,a2,a3,a4,a6]
j	-273359449/1536000	j-invariant
L	1.1583921113141	L(r)(E,1)/r!
Ω	1.1583921113141	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	30a3 960o3 720j3 1200p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240b3

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
-	+	+	4	0	2	6	4	0	-6	-8	2	-6	4	0	-6	0	-10	4	0	2	-8	-12	18	2

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Quadratic twists for elliptic curve 240b3

-4	8	-3	5	-7	-11	13	17	-19	-23
30a3	960o3	720j3	1200p3	11760cp3	29040ch3	40560bv3	69360du3	86640dq3	126960ch3

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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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