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	2088d	Isogeny class
Conductor	2088	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-21648384 = -1 · 210 · 36 · 29	Discriminant
Eigenvalues	2+ 3- -1  2 -3 -1  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-723,7486]	[a1,a2,a3,a4,a6]
Generators	[15:4:1]	Generators of the group modulo torsion
j	-55990084/29	j-invariant
L	2.9904685289577	L(r)(E,1)/r!
Ω	2.1208181122626	Real period
R	0.70502710997863	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	4176h1 16704q1 232b1 52200ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2088d1

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
+	-	-1	2	-3	-1	0	0	-4	-	3	-8	6	-5	-3	-5	8	0	-12	-6	-4	1	12	-6	14

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Quadratic twists for elliptic curve 2088d1

-4	8	-3	5	-7	29
4176h1	16704q1	232b1	52200ca1	102312o1	60552o1

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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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