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	1288i	Isogeny class
Conductor	1288	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	127459985408 = 211 · 76 · 232	Discriminant
Eigenvalues	2-  2  2 7-  2  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2672,51212]	[a1,a2,a3,a4,a6]
j	1030541881826/62236321	j-invariant
L	3.0767170335955	L(r)(E,1)/r!
Ω	1.0255723445318	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	2576c2 10304p2 11592e2 32200b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288i2

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	2	-	2	4	-2	0	-	-2	0	-4	6	2	4	0	2	-10	2	-8	-6	0	0	10	10

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Quadratic twists for elliptic curve 1288i2

-4	8	-3	5	-7	-23
2576c2	10304p2	11592e2	32200b2	9016n2	29624l2

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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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