Cremona's table of elliptic curves

2873 = 13² · 17

Field	Data	Notes
Atkin-Lehner	13+ 17-	Signs for the Atkin-Lehner involutions
Class	2873b	Isogeny class
Conductor	2873	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	396067447082177 = 1312 · 17	Discriminant
Eigenvalues	1  0 -4  2 -6 13+ 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-123824,16774499]	[a1,a2,a3,a4,a6]
j	43499078731809/82055753	j-invariant
L	0.5339058638063	L(r)(E,1)/r!
Ω	0.5339058638063	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45968r1 25857j1 71825g1 221a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2873b1

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

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Quadratic twists for elliptic curve 2873b1

-4	-3	5	13	17
45968r1	25857j1	71825g1	221a1	48841b1

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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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