Cremona's table of elliptic curves

1517 = 37 · 41

Field	Data	Notes
Atkin-Lehner	37+ 41-	Signs for the Atkin-Lehner involutions
Class	1517a	Isogeny class
Conductor	1517	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	175753856917 = 37 · 416	Discriminant
Eigenvalues	1  0 -2 -4  4  4  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1633,-15036]	[a1,a2,a3,a4,a6]
j	481761237764457/175753856917	j-invariant
L	1.160892314646	L(r)(E,1)/r!
Ω	0.77392820976397	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	24272d2 97088i2 13653a2 37925f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1517a2

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	-2	-4	4	4	0	6	-4	0	8	+	-	-4	0	10	-4	10	8	-12	14	-14	12	16	-8

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Quadratic twists for elliptic curve 1517a2

-4	8	-3	5	-7	37	41
24272d2	97088i2	13653a2	37925f2	74333c2	56129b2	62197a2

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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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