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	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-3840 = -1 · 28 · 3 · 5	Discriminant
Eigenvalues	2+ 3+ 5+ -4  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4,0]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	21296/15	j-invariant
L	1.2467793270684	L(r)(E,1)/r!
Ω	2.7966571709541	Real period
R	0.89162113970738	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	120b1 960p1 720e1 1200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 240c1

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 240c1

-4	8	-3	5	-7	-11	13	17	-19	-23
120b1	960p1	720e1	1200g1	11760bf1	29040j1	40560k1	69360bt1	86640u1	126960l1

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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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