Cremona's table of elliptic curves

3045 = 3 · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 29-	Signs for the Atkin-Lehner involutions
Class	3045g	Isogeny class
Conductor	3045	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2005141635 = -1 · 34 · 5 · 7 · 294	Discriminant
Eigenvalues	-1 3- 5+ 7+ -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,29,2156]	[a1,a2,a3,a4,a6]
Generators	[-5:46:1]	Generators of the group modulo torsion
j	2691419471/2005141635	j-invariant
L	2.3126877099309	L(r)(E,1)/r!
Ω	1.1496614114067	Real period
R	0.50290626591986	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	48720bl3 9135g4 15225d4 21315i3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045g4

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

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Quadratic twists for elliptic curve 3045g4

-4	-3	5	-7	29
48720bl3	9135g4	15225d4	21315i3	88305a3

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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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