Cremona's table of elliptic curves

1088 = 2⁶ · 17

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	1088d	Isogeny class
Conductor	1088	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	1114112 = 216 · 17	Discriminant
Eigenvalues	2+ -2  0  0 -2  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,-65]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1]	Generators of the group modulo torsion
j	62500/17	j-invariant
L	1.9045208944872	L(r)(E,1)/r!
Ω	2.027460174407	Real period
R	0.93936291253871	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	1088g1 136b1 9792o1 27200y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1088d1

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	0	0	-2	6	+	-4	4	0	-8	4	6	-8	-8	-10	0	-12	-8	12	2	-4	-16	10	-18

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Quadratic twists for elliptic curve 1088d1

-4	8	-3	5	-7	17
1088g1	136b1	9792o1	27200y1	53312x1	18496d1

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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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