Cremona's table of elliptic curves

6840 = 2³ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	6840s	Isogeny class
Conductor	6840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	526338000 = 24 · 36 · 53 · 192	Discriminant
Eigenvalues	2- 3- 5+  0  4  4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-318,-1883]	[a1,a2,a3,a4,a6]
j	304900096/45125	j-invariant
L	2.2835046570083	L(r)(E,1)/r!
Ω	1.1417523285041	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	13680h1 54720bp1 760d1 34200bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840s1

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
-	-	+	0	4	4	2	-	4	6	-8	-4	2	4	8	0	8	2	-14	8	6	-4	-16	18	-4

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Quadratic twists for elliptic curve 6840s1

-4	8	-3	5	-19
13680h1	54720bp1	760d1	34200bb1	129960q1

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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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