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	840c	Isogeny class
Conductor	840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2822400 = 28 · 32 · 52 · 72	Discriminant
Eigenvalues	2+ 3+ 5- 7+  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-140,-588]	[a1,a2,a3,a4,a6]
j	1193895376/11025	j-invariant
L	1.3878783222606	L(r)(E,1)/r!
Ω	1.3878783222606	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	1680i2 6720p2 2520o2 4200z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840c2

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	2	2	0	0	6	4	-2	10	4	0	2	4	6	-12	12	-2	0	4	10	-2

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Quadratic twists for elliptic curve 840c2

-4	8	-3	5	-7	-11
1680i2	6720p2	2520o2	4200z2	5880k2	101640ce2

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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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