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	1287a	Isogeny class
Conductor	1287	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	15769185003 = 33 · 112 · 136	Discriminant
Eigenvalues	-1 3+  2 -2 11+ 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1799,-28284]	[a1,a2,a3,a4,a6]
Generators	[-22:27:1]	Generators of the group modulo torsion
j	23835655373139/584043889	j-invariant
L	1.8610839759947	L(r)(E,1)/r!
Ω	0.73419133737676	Real period
R	1.2674379832948	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	20592v2 82368n2 1287b2 32175b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1287a2

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 1287a2

-4	8	-3	5	-7	-11	13
20592v2	82368n2	1287b2	32175b2	63063h2	14157e2	16731c2

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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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