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
deg	744	Modular degree for the optimal curve
Δ	94352849 = 372 · 413	Discriminant
Eigenvalues	1  0 -2 -4  4  4  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1448,-20845]	[a1,a2,a3,a4,a6]
j	335890789988697/94352849	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	24272d1 97088i1 13653a1 37925f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1517a1

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 1517a1

-4	8	-3	5	-7	37	41
24272d1	97088i1	13653a1	37925f1	74333c1	56129b1	62197a1

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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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