Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	840j	Isogeny class
Conductor	840	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	13829760000 = 210 · 32 · 54 · 74	Discriminant
Eigenvalues	2- 3- 5- 7+  4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-600,0]	[a1,a2,a3,a4,a6]
j	23366901604/13505625	j-invariant
L	2.128934407385	L(r)(E,1)/r!
Ω	1.0644672036925	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1680d4 6720e3 2520f4 4200d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840j3

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

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Quadratic twists for elliptic curve 840j3

-4	8	-3	5	-7	-11
1680d4	6720e3	2520f4	4200d3	5880t4	101640bm3

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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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