Cremona's table of elliptic curves

6675 = 3 · 5² · 89

Field	Data	Notes
Atkin-Lehner	3+ 5+ 89-	Signs for the Atkin-Lehner involutions
Class	6675f	Isogeny class
Conductor	6675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	111000	Modular degree for the optimal curve
Δ	-167784326884950075 = -1 · 325 · 52 · 892	Discriminant
Eigenvalues	-2 3+ 5+ -3  4 -3  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-302288,67038218]	[a1,a2,a3,a4,a6]
j	-122193431714654556160/6711373075398003	j-invariant
L	0.6362903408931	L(r)(E,1)/r!
Ω	0.31814517044655	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106800bz1 20025k1 6675j1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6675f1

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	+	+	-3	4	-3	0	5	4	6	-1	10	0	-7	0	2	6	-7	3	-12	6	16	0	-	3

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Quadratic twists for elliptic curve 6675f1

-4	-3	5
106800bz1	20025k1	6675j1

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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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