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	1287c	Isogeny class
Conductor	1287	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-938223 = -1 · 38 · 11 · 13	Discriminant
Eigenvalues	1 3-  0  0 11+ 13-  4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,18,-41]	[a1,a2,a3,a4,a6]
Generators	[6:13:1]	Generators of the group modulo torsion
j	857375/1287	j-invariant
L	3.175929504917	L(r)(E,1)/r!
Ω	1.4778191191852	Real period
R	2.1490651079599	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	20592bq1 82368bm1 429a1 32175j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1287c1

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	-	0	0	+	-	4	-8	0	-4	-6	-6	-6	-2	8	-6	0	-14	14	4	6	-10	12	-12	-2

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Quadratic twists for elliptic curve 1287c1

-4	8	-3	5	-7	-11	13
20592bq1	82368bm1	429a1	32175j1	63063m1	14157k1	16731l1

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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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