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	3	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-773344 = -1 · 25 · 11 · 133	Discriminant
Eigenvalues	2+ -2  3 -1 11+ 13-  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7,42]	[a1,a2,a3,a4,a6]
j	-30664297/773344	j-invariant
L	0.79220583897341	L(r)(E,1)/r!
Ω	2.3766175169202	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2288l1 9152j1 2574y1 7150p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 286a1

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 286a1

-4	8	-3	5	-7	-11	13	17	-19
2288l1	9152j1	2574y1	7150p1	14014b1	3146n1	3718q1	82654i1	103246l1

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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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