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	164025 = 38 · 52	Discriminant
Eigenvalues	-1 3+ 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-135,-660]	[a1,a2,a3,a4,a6]
j	272223782641/164025	j-invariant
L	0.35015076058315	L(r)(E,1)/r!
Ω	1.4006030423326	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	240d5 960g5 45a5 75b5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15a2

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 15a2

-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
240d5	960g5	45a5	75b5	735e5	1815a5	2535a5	4335d5	5415k5	7935b5	12615f5	14415g5	20535a5	25215h6	27735g6	33135a6	42135f6	52215d6	55815c6	67335g6	75615e6	79935a6	93615n6	103335d6	118815c6

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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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