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	6840c	Isogeny class
Conductor	6840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	9095120640000 = 211 · 39 · 54 · 192	Discriminant
Eigenvalues	2+ 3+ 5-  4 -2 -4  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5427,51246]	[a1,a2,a3,a4,a6]
j	438512454/225625	j-invariant
L	2.5758408951521	L(r)(E,1)/r!
Ω	0.64396022378803	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	13680f2 54720f2 6840k2 34200by2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840c2

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	-2	-4	4	+	0	2	2	-8	6	12	-12	-2	-12	14	16	8	6	2	10	14	-6

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Quadratic twists for elliptic curve 6840c2

-4	8	-3	5	-19
13680f2	54720f2	6840k2	34200by2	129960bu2

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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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