Cremona's table of elliptic curves

1517 = 37 · 41

Field	Data	Notes
Atkin-Lehner	37- 41+	Signs for the Atkin-Lehner involutions
Class	1517b	Isogeny class
Conductor	1517	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-1517 = -1 · 37 · 41	Discriminant
Eigenvalues	-1  1  4  4 -3  5  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1,-2]	[a1,a2,a3,a4,a6]
j	-117649/1517	j-invariant
L	2.036568260808	L(r)(E,1)/r!
Ω	2.036568260808	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24272f1 97088d1 13653b1 37925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1517b1

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	1	4	4	-3	5	3	2	1	-6	0	-	+	1	9	-12	-7	-8	3	-8	-13	-4	6	-1	-10

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Quadratic twists for elliptic curve 1517b1

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

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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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