Cremona's table of elliptic curves

6678 = 2 · 3² · 7 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 53+	Signs for the Atkin-Lehner involutions
Class	6678r	Isogeny class
Conductor	6678	Conductor
∏ cp	200	Product of Tamagawa factors cp
deg	134400	Modular degree for the optimal curve
Δ	-98996801564408832 = -1 · 210 · 36 · 75 · 534	Discriminant
Eigenvalues	2- 3-  4 7-  0 -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-266513,-55011711]	[a1,a2,a3,a4,a6]
j	-2871771293482144201/135798081707008	j-invariant
L	5.2385754534057	L(r)(E,1)/r!
Ω	0.10477150906811	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53424z1 742e1 46746bk1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6678r1

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
-	-	4	-	0	-4	2	6	8	6	-8	-6	-2	-8	-4	+	-2	12	-4	8	-2	8	-6	-2	-2

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Quadratic twists for elliptic curve 6678r1

-4	-3	-7
53424z1	742e1	46746bk1

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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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