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
deg	384	Modular degree for the optimal curve
Δ	380625 = 3 · 54 · 7 · 29	Discriminant
Eigenvalues	-1 3- 5+ 7+ -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21,-24]	[a1,a2,a3,a4,a6]
Generators	[5:-1:1]	Generators of the group modulo torsion
j	1027243729/380625	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	48720bl1 9135g1 15225d1 21315i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045g1

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 3045g1

-4	-3	5	-7	29
48720bl1	9135g1	15225d1	21315i1	88305a1

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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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