Cremona's table of elliptic curves

286 = 2 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13-	Signs for the Atkin-Lehner involutions
Class	286a	Isogeny class
Conductor	286	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-566984704 = -1 · 215 · 113 · 13	Discriminant
Eigenvalues	2+ -2  3 -1 11+ 13-  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,58,-1128]	[a1,a2,a3,a4,a6]
j	22117051943/566984704	j-invariant
L	0.79220583897341	L(r)(E,1)/r!
Ω	0.79220583897341	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2288l2 9152j2 2574y2 7150p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 286a2

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	3	-1	+	-	6	8	-3	9	2	-10	9	-1	0	6	-3	-7	-7	12	-1	-4	0	12	-4

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Quadratic twists for elliptic curve 286a2

-4	8	-3	5	-7	-11	13	17	-19
2288l2	9152j2	2574y2	7150p2	14014b2	3146n2	3718q2	82654i2	103246l2

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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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