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	8	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	50625 = 34 · 54	Discriminant
Eigenvalues	-1 3+ 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-10,-10]	[a1,a2,a3,a4,a6]
j	111284641/50625	j-invariant
L	0.35015076058315	L(r)(E,1)/r!
Ω	2.8012060846652	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	240d4 960g3 45a4 75b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15a1

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 15a1

-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
240d4	960g3	45a4	75b3	735e4	1815a4	2535a3	4335d3	5415k4	7935b4	12615f3	14415g4	20535a3	25215h3	27735g3	33135a3	42135f3	52215d3	55815c3	67335g3	75615e3	79935a3	93615n3	103335d3	118815c3

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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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