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	1288d	Isogeny class
Conductor	1288	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	2770869248 = 210 · 76 · 23	Discriminant
Eigenvalues	2+  2  4 7-  4 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-376,-1092]	[a1,a2,a3,a4,a6]
j	5756278756/2705927	j-invariant
L	3.4040051867981	L(r)(E,1)/r!
Ω	1.1346683955994	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2576d2 10304k2 11592s2 32200r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288d2

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	4	-	4	-2	-4	0	+	2	-6	2	-6	-4	-10	6	-2	8	-4	-16	6	0	12	-4	-8

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Quadratic twists for elliptic curve 1288d2

-4	8	-3	5	-7	-23
2576d2	10304k2	11592s2	32200r2	9016e2	29624e2

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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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