Cremona's table of elliptic curves

336 = 2⁴ · 3 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7-	Signs for the Atkin-Lehner involutions
Class	336b	Isogeny class
Conductor	336	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-7375872 = -1 · 210 · 3 · 74	Discriminant
Eigenvalues	2+ 3+  2 7-  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,48,-48]	[a1,a2,a3,a4,a6]
j	11696828/7203	j-invariant
L	1.3590628922507	L(r)(E,1)/r!
Ω	1.3590628922507	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	168a4 1344t4 1008g4 8400r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 336b4

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

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Quadratic twists for elliptic curve 336b4

-4	8	-3	5	-7	-11	13	17	-19
168a4	1344t4	1008g4	8400r4	2352i4	40656i3	56784b3	97104s3	121296bm3

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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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