Cremona's table of elliptic curves

1045 = 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	5+ 11+ 19+	Signs for the Atkin-Lehner involutions
Class	1045a	Isogeny class
Conductor	1045	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	5225 = 52 · 11 · 19	Discriminant
Eigenvalues	-1 -2 5+ -2 11+  6  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6,-5]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	24137569/5225	j-invariant
L	1.0588475231503	L(r)(E,1)/r!
Ω	3.0946515238653	Real period
R	0.68430808120702	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16720z1 66880bv1 9405m1 5225a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1045a1

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

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Quadratic twists for elliptic curve 1045a1

-4	8	-3	5	-7	-11	-19
16720z1	66880bv1	9405m1	5225a1	51205o1	11495c1	19855a1

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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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