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	1045b	Isogeny class
Conductor	1045	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	2223652969140625 = 58 · 112 · 196	Discriminant
Eigenvalues	1  0 5-  0 11+  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-982414,-374539305]	[a1,a2,a3,a4,a6]
Generators	[5206:365617:1]	Generators of the group modulo torsion
j	104859453317683374662841/2223652969140625	j-invariant
L	3.0277046455138	L(r)(E,1)/r!
Ω	0.15164442574915	Real period
R	3.3276359379917	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16720bh2 66880m2 9405i2 5225b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1045b2

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

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Quadratic twists for elliptic curve 1045b2

-4	8	-3	5	-7	-11	-19
16720bh2	66880m2	9405i2	5225b2	51205d2	11495f2	19855c2

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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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