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	405 = 34 · 5	Discriminant
Eigenvalues	-1 3+ 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2160,-39540]	[a1,a2,a3,a4,a6]
j	1114544804970241/405	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	240d7 960g7 45a7 75b7	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15a5

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 15a5

-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
240d7	960g7	45a7	75b7	735e7	1815a7	2535a7	4335d7	5415k7	7935b7	12615f7	14415g7	20535a7	25215h8	27735g8	33135a8	42135f8	52215d8	55815c8	67335g8	75615e8	79935a8	93615n8	103335d8	118815c8

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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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