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	4	Product of Tamagawa factors cp
Δ	218405 = 5 · 112 · 192	Discriminant
Eigenvalues	-1 -2 5+ -2 11+  6  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-31,60]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1]	Generators of the group modulo torsion
j	3301293169/218405	j-invariant
L	1.0588475231503	L(r)(E,1)/r!
Ω	3.0946515238653	Real period
R	0.34215404060351	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	16720z2 66880bv2 9405m2 5225a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1045a2

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 1045a2

-4	8	-3	5	-7	-11	-19
16720z2	66880bv2	9405m2	5225a2	51205o2	11495c2	19855a2

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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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