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	840a	Isogeny class
Conductor	840	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	38093690880 = 211 · 312 · 5 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1736,26796]	[a1,a2,a3,a4,a6]
Generators	[33:66:1]	Generators of the group modulo torsion
j	282678688658/18600435	j-invariant
L	1.9611172164749	L(r)(E,1)/r!
Ω	1.132048714962	Real period
R	3.4647223048892	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1680g3 6720bb3 2520r3 4200ba3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840a3

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

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Quadratic twists for elliptic curve 840a3

-4	8	-3	5	-7	-11
1680g3	6720bb3	2520r3	4200ba3	5880p3	101640bv4

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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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