Cremona's table of elliptic curves

1088 = 2⁶ · 17

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	1088j	Isogeny class
Conductor	1088	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	69632 = 212 · 17	Discriminant
Eigenvalues	2- -2 -4 -4 -2 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-25,39]	[a1,a2,a3,a4,a6]
Generators	[-5:8:1] [-1:8:1]	Generators of the group modulo torsion
j	438976/17	j-invariant
L	1.828332935864	L(r)(E,1)/r!
Ω	3.4388774203904	Real period
R	0.53166563164489	Regulator
r	2	Rank of the group of rational points
S	1.0000000000015	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1088h1 544e1 9792ce1 27200ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1088j1

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	-2	+	-8	-8	-4	-4	8	-2	4	0	6	-4	-8	-4	-8	-6	0	4	-6	-2

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Quadratic twists for elliptic curve 1088j1

-4	8	-3	5	-7	17
1088h1	544e1	9792ce1	27200ck1	53312ce1	18496q1

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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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