Cremona's table of elliptic curves

15 = 3 · 5

Field	Data	Notes
Atkin-Lehner	3+ 5-	Signs for the Atkin-Lehner involutions
Class	15a	Isogeny class
Conductor	15	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	225 = 32 · 52	Discriminant
Eigenvalues	-1 3+ 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5,2]	[a1,a2,a3,a4,a6]
j	13997521/225	j-invariant
L	0.35015076058315	L(r)(E,1)/r!
Ω	5.6024121693304	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	240d2 960g2 45a2 75b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15a3

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
-1	+	-	0	-4	-2	2	4	0	-2	0	-10	10	4	8	-10	-4	-2	12	-8	10	0	12	-6	2

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Quadratic twists for elliptic curve 15a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83	89
240d2	960g2	45a2	75b2	735e2	1815a2	2535a2	4335d2	5415k2	7935b2	12615f2	14415g2	20535a2	25215h2	27735g2	33135a2	42135f2	52215d2	55815c2	67335g2	75615e2	79935a2	93615n2	103335d2	118815c2

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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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