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	2	Product of Tamagawa factors cp
Δ	-215233605 = -1 · 316 · 5	Discriminant
Eigenvalues	-1 3+ 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-110,-880]	[a1,a2,a3,a4,a6]
j	-147281603041/215233605	j-invariant
L	0.35015076058315	L(r)(E,1)/r!
Ω	0.7003015211663	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	240d8 960g8 45a8 75b8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15a6

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 15a6

-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
240d8	960g8	45a8	75b8	735e8	1815a8	2535a8	4335d8	5415k8	7935b8	12615f8	14415g8	20535a8	25215h7	27735g7	33135a7	42135f7	52215d7	55815c7	67335g7	75615e7	79935a7	93615n7	103335d7	118815c7

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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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