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	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-868489479 = -1 · 33 · 114 · 133	Discriminant
Eigenvalues	-1 3+  2 -2 11+ 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,16,-1422]	[a1,a2,a3,a4,a6]
Generators	[14:30:1]	Generators of the group modulo torsion
j	17779581/32166277	j-invariant
L	1.8610839759947	L(r)(E,1)/r!
Ω	0.73419133737676	Real period
R	2.5348759665897	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	20592v1 82368n1 1287b1 32175b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1287a1

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

---

Quadratic twists for elliptic curve 1287a1

-4	8	-3	5	-7	-11	13
20592v1	82368n1	1287b1	32175b1	63063h1	14157e1	16731c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations