Cremona's table of elliptic curves

1088 = 2⁶ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	1088a	Isogeny class
Conductor	1088	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	69632 = 212 · 17	Discriminant
Eigenvalues	2+  0  0  2 -4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20,-32]	[a1,a2,a3,a4,a6]
Generators	[-3:1:1]	Generators of the group modulo torsion
j	216000/17	j-invariant
L	2.5077049444601	L(r)(E,1)/r!
Ω	2.2688378967211	Real period
R	1.1052816722095	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	1088b1 544d1 9792s1 27200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1088a1

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

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Quadratic twists for elliptic curve 1088a1

-4	8	-3	5	-7	17
1088b1	544d1	9792s1	27200s1	53312r1	18496b1

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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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