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	2	Product of Tamagawa factors cp
Δ	1044435 = 3 · 5 · 74 · 29	Discriminant
Eigenvalues	-1 3- 5+ 7+ -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2321,42846]	[a1,a2,a3,a4,a6]
Generators	[30:6:1]	Generators of the group modulo torsion
j	1382804639990929/1044435	j-invariant
L	2.3126877099309	L(r)(E,1)/r!
Ω	2.2993228228135	Real period
R	2.0116250636794	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	48720bl4 9135g3 15225d3 21315i4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045g3

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 3045g3

-4	-3	5	-7	29
48720bl4	9135g3	15225d3	21315i4	88305a4

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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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