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	322a	Isogeny class
Conductor	322	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	5411854 = 2 · 76 · 23	Discriminant
Eigenvalues	2+  0 -2 7- -4  4 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-238,1470]	[a1,a2,a3,a4,a6]
Generators	[7:7:1]	Generators of the group modulo torsion
j	1494447319737/5411854	j-invariant
L	1.2132690207407	L(r)(E,1)/r!
Ω	2.4232379290347	Real period
R	0.33378728689236	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	2576j2 10304l2 2898q2 8050n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 322a2

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

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Quadratic twists for elliptic curve 322a2

-4	8	-3	5	-7	-11	13	17	-19	-23
2576j2	10304l2	2898q2	8050n2	2254b2	38962bd2	54418g2	93058a2	116242y2	7406b2

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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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