Cremona's table of elliptic curves

1288 = 2³ · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	1288f	Isogeny class
Conductor	1288	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	306031424964608 = 211 · 710 · 232	Discriminant
Eigenvalues	2+ -2  0 7-  0  0 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16968,118384]	[a1,a2,a3,a4,a6]
Generators	[203:2254:1]	Generators of the group modulo torsion
j	263822189935250/149429406721	j-invariant
L	2.0169859967984	L(r)(E,1)/r!
Ω	0.46906591518023	Real period
R	0.86000109218057	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	2576b2 10304n2 11592p2 32200p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288f2

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
+	-2	0	-	0	0	-6	6	-	-6	8	2	-2	-8	-8	-2	-6	0	-12	-8	-6	-16	6	6	-14

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Quadratic twists for elliptic curve 1288f2

-4	8	-3	5	-7	-23
2576b2	10304n2	11592p2	32200p2	9016h2	29624f2

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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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