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	1287d	Isogeny class
Conductor	1287	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-1355211 = -1 · 36 · 11 · 132	Discriminant
Eigenvalues	0 3-  1 -2 11- 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-12,58]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	-262144/1859	j-invariant
L	2.3307494465994	L(r)(E,1)/r!
Ω	2.3276133876236	Real period
R	0.50067366406131	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20592bb1 82368bg1 143a1 32175t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1287d1

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
0	-	1	-2	-	+	4	2	-7	2	-3	-11	-10	-4	4	-2	1	-2	-1	9	-16	8	0	7	-13

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Quadratic twists for elliptic curve 1287d1

-4	8	-3	5	-7	-11	13
20592bb1	82368bg1	143a1	32175t1	63063y1	14157q1	16731e1

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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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