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	3045a	Isogeny class
Conductor	3045	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1840	Modular degree for the optimal curve
Δ	-13321875 = -1 · 3 · 55 · 72 · 29	Discriminant
Eigenvalues	2 3+ 5+ 7+  5 -4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-166,-789]	[a1,a2,a3,a4,a6]
Generators	[202:815:8]	Generators of the group modulo torsion
j	-508934139904/13321875	j-invariant
L	5.1652266909463	L(r)(E,1)/r!
Ω	0.66367227959884	Real period
R	3.8913985484435	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48720cg1 9135i1 15225w1 21315t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045a1

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
2	+	+	+	5	-4	6	-8	1	+	-2	-5	-11	-9	4	11	6	-12	-12	16	-1	-14	-15	-10	9

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Quadratic twists for elliptic curve 3045a1

-4	-3	5	-7	29
48720cg1	9135i1	15225w1	21315t1	88305n1

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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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