Cremona's table of elliptic curves

2088 = 2³ · 3² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 29-	Signs for the Atkin-Lehner involutions
Class	2088g	Isogeny class
Conductor	2088	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-853419888 = -1 · 24 · 37 · 293	Discriminant
Eigenvalues	2+ 3- -4  3 -1  1  1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-327,2675]	[a1,a2,a3,a4,a6]
Generators	[43:261:1]	Generators of the group modulo torsion
j	-331527424/73167	j-invariant
L	2.6606246872238	L(r)(E,1)/r!
Ω	1.5123898711231	Real period
R	0.14660156628176	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	4176m1 16704bd1 696e1 52200cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2088g1

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
+	-	-4	3	-1	1	1	-4	2	-	-10	6	-6	4	3	-4	-10	-14	-7	-2	-2	16	-2	-9	-16

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Quadratic twists for elliptic curve 2088g1

-4	8	-3	5	-7	29
4176m1	16704bd1	696e1	52200cd1	102312t1	60552u1

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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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