Cremona's table of elliptic curves

322 = 2 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	322d	Isogeny class
Conductor	322	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	829472 = 25 · 72 · 232	Discriminant
Eigenvalues	2- -2 -2 7+ -2 -4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-174,868]	[a1,a2,a3,a4,a6]
Generators	[2:22:1]	Generators of the group modulo torsion
j	582810602977/829472	j-invariant
L	1.6590507173596	L(r)(E,1)/r!
Ω	2.8164413550461	Real period
R	0.11781184183986	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	2576p2 10304d2 2898d2 8050i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 322d2

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

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Quadratic twists for elliptic curve 322d2

-4	8	-3	5	-7	-11	13	17	-19	-23
2576p2	10304d2	2898d2	8050i2	2254f2	38962q2	54418d2	93058m2	116242g2	7406i2

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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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