Cremona's table of elliptic curves

1287 = 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	3+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	1287b	Isogeny class
Conductor	1287	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-633128830191 = -1 · 39 · 114 · 133	Discriminant
Eigenvalues	1 3+ -2 -2 11- 13+  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,147,38240]	[a1,a2,a3,a4,a6]
j	17779581/32166277	j-invariant
L	1.429982381301	L(r)(E,1)/r!
Ω	0.71499119065051	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592q1 82368d1 1287a1 32175f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1287b1

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
1	+	-2	-2	-	+	4	6	8	0	10	-6	-2	0	8	0	-4	-6	-10	0	10	-4	12	18	-10

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Quadratic twists for elliptic curve 1287b1

-4	8	-3	5	-7	-11	13
20592q1	82368d1	1287a1	32175f1	63063j1	14157f1	16731a1

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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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