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	1288h	Isogeny class
Conductor	1288	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-9538928 = -1 · 24 · 72 · 233	Discriminant
Eigenvalues	2- -3 -4 7+  2  5  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,53,-5]	[a1,a2,a3,a4,a6]
Generators	[29:161:1]	Generators of the group modulo torsion
j	1029037824/596183	j-invariant
L	1.3251405868626	L(r)(E,1)/r!
Ω	1.3681121732338	Real period
R	0.080715883097165	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	2576g1 10304g1 11592c1 32200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288h1

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
-	-3	-4	+	2	5	0	-4	-	-3	5	4	5	-4	-11	0	-12	-6	-16	7	7	16	8	-12	6

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Quadratic twists for elliptic curve 1288h1

-4	8	-3	5	-7	-23
2576g1	10304g1	11592c1	32200g1	9016o1	29624q1

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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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