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	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	9573811200 = 210 · 39 · 52 · 19	Discriminant
Eigenvalues	2+ 3+ 5-  4 -2 -4  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4347,110214]	[a1,a2,a3,a4,a6]
j	450714348/475	j-invariant
L	2.5758408951521	L(r)(E,1)/r!
Ω	1.2879204475761	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	13680f1 54720f1 6840k1 34200by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840c1

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 6840c1

-4	8	-3	5	-19
13680f1	54720f1	6840k1	34200by1	129960bu1

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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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