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	240c	Isogeny class
Conductor	240	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	230400 = 210 · 32 · 52	Discriminant
Eigenvalues	2+ 3+ 5+ -4  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16,16]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	470596/225	j-invariant
L	1.2467793270684	L(r)(E,1)/r!
Ω	2.7966571709541	Real period
R	0.44581056985369	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	120b2 960p2 720e2 1200g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240c2

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	-6	-2	-4	8	-6	0	-6	10	4	-8	10	0	6	4	0	-14	-16	-12	2	2

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Quadratic twists for elliptic curve 240c2

-4	8	-3	5	-7	-11	13	17	-19	-23
120b2	960p2	720e2	1200g2	11760bf2	29040j2	40560k2	69360bt2	86640u2	126960l2

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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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